'''
Created on 20-Jan-2022

@author: bthakur
'''

import inspect
import traceback
import random
import numpy as np
from sympy import (latex, Symbol, symbols,
                   Eq, Rational,
                   UnevaluatedExpr as ueval,
                   )

from xv.util import toIntOrFloat, listAttr
from xv.km.storeddata import BaseStoredQuestions
from xv.km import CustomLogarithm as Log
from xv.km.util import latex_log, latex_fraction, latex_exponent

# _amc8_stored_questions
# Amc8StoredQuestions

class Amc8StoredQuestions(BaseStoredQuestions):
    _QUESTION_KEYWORDS = None
    
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        pass
       
    def get_question_2022_1(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_1',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?
        <img src="https://latex.artofproblemsolving.com/a/a/8/aa8ae8c181def4cc4946be20a97f03d34db3ea20.png">
        (A) 10
        (B) 12
        (C) 13
        (D) 14
        (E) 15
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_2(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_2',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Consider these two operations:
        $\begin{{gathered}} a \diamond b=a^2-b^2 \\ a \star b=(a-b)^2 \end{{gathered}}$
        What is the value of $(5 \diamond 3) \star 6 ?$
        (A) $-20$
        (B) 4
        (C) 16
        (D) 100
        (E) 220

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_3(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_3',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        When three positive integers $a, b$, and $c$ are multiplied together, their product is 100 . Suppose $a<b<c$. In how many ways can the numbers be chosen?
        (A) 0
        (B) 1
        (C) 2
        (D) 3
        (E) 4

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_4(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_4',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The letter $\mathbf{{M}}$ in the figure below is first reflected over the line $q$ and then reflected over the line $p$. What is the resulting image?
        <img src="https://latex.artofproblemsolving.com/c/3/8/c38b67d113d5fbf1b6d6eae0d87161b539dbd849.png">
        
        <img src="https://latex.artofproblemsolving.com/1/9/b/19b58c8f6aafe00e0ad5454583fda04c3567f944.png">

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_5(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_5',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned 6 years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is 30 years. How many years older than Bella is Anna?
        (A) 1
        (B) 2
        (C) 3
        (D) 4
        (E) 5

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_6(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_6',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Three positive integers are equally spaced on a number line. The middle number is 15 , and the largest number is 4 times the smallest number. What is the smallest of these three numbers?
        (A) 4
        (B) 5
        (C) 6
        (D) 7
        (E) 8

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_7(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_7',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        When the World Wide Web first became popular in the 1990s, download speeds reached a maximum of about 56 kilobits per second.
        Approximately how many minutes would the download of a 4.2-megabyte song have taken at that speed? (Note that there are 8000 kilobits in a megabyte.)
        (A) $0.6$
        (B) 10
        (C) 1800
        (D) 7200
        (E) 36000
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_8(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_8',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        What is the value of
        $\displaystyle \frac{{1}}{{3}} \cdot \frac{{2}}{{4}} \cdot \frac{{3}}{{5}} \cdots \frac{{18}}{{20}} \cdot \frac{{19}}{{21}} \cdot \frac{{20}}{{22}} ?$
        
        (A) $\displaystyle \frac{{1}}{{462}}$
        
        (B) $\displaystyle \frac{{1}}{{231}}$
        
        (C) $\displaystyle \frac{{1}}{{132}}$
        
        (D) $\displaystyle \frac{{2}}{{213}}$
        
        (E) $\displaystyle \frac{{1}}{{22}}$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_9(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_9',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A cup of boiling water $\left(212^{{\circ}} \mathrm{{F}}\right)$ is placed to cool in a room whose temperature remains constant at $68^{{\circ}} \mathrm{{F}}$. Suppose the difference between the water temperature and the room temperature is halved every 5 minutes. What is the water temperature, in degrees Fahrenheit, after 15 minutes?
        (A) 77
        (B) 86
        (C) 92
        (D) 98
        (E) 104
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_10(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_10',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        One sunny day, Ling decided to take a hike in the mountains. She left her house at $8 \mathrm{{AM}}$, drove at a constant speed of 45 miles per hour, and arrived at the hiking trail at 10 AM. After hiking for 3 hours, Ling drove home at a constant speed of 60 miles per hour. Which of the following graphs best illustrates the distance between Ling's car and her house over the course of her trip?

        <img src="https://latex.artofproblemsolving.com/c/b/1/cb1e2b28781a01015ec88e8948e5bda92a234383.png">

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_11(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_11',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating 3 inches of pasta from the middle of one piece. In the end, he has 10 pieces of pasta whose total length is 17 inches. How long, in inches, was the piece of pasta he started with?
        (A) 34
        (B) 38
        (C) 41
        (D) 44
        (E) 47
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_12(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_12',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The arrows on the two spinners shown below are spun. Let the number $N$ equal 10 times the number on Spinner A, added to the number on Spinner B. What is the probability that $N$ is a perfect square number?
        <img src="https://latex.artofproblemsolving.com/5/5/2/552b70fd0a4e9d6d464f53f730e82883afd5b278.png">
        
        (A) $\displaystyle \frac{{1}}{{16}}$
        
        (B) $\displaystyle \frac{{1}}{{8}}$
        
        (C) $\displaystyle \frac{{1}}{{4}}$
        
        (D) $\displaystyle \frac{{3}}{{8}}$
        
        (E) $\displaystyle \frac{{1}}{{2}}$

        
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_13(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_13',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        How many positive integers can fill the blank in the sentence below?
        "One positive integer is ____ more than twice another, and the sum of the two numbers is $28 . "$
        (A) 6
        (B) 7
        (C) 8
        (D) 9
        (E) 10
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_14(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_14',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        In how many ways can the letters in BEEKEEPER be rearranged so that two or more Es do not appear together?
        (A) 1
        (B) 4
        (C) 12
        (D) 24
        (E) 120
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_15(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_15',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price, shown in the scatter plot below. In ounces, what is the weight of the pepper that offers the lowest price per ounce?
        <img src="https://latex.artofproblemsolving.com/6/a/5/6a53d139336647bb978d693c547d713dd1f48d5f.png">
        (A) 1
        (B) 2
        (C) 3
        (D) 4
        (E) 5
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_16(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_16',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Four numbers are written in a row. The average of the first two is 21 , the average of the middle two is 26 , and the average of the last two is 30 . What is the average of the first and last of the numbers?
        (A) 24
        (B) 25
        (C) 26
        (D) 27
        (E) 28

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_17(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_17',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        If $n$ is an even positive integer, the double factorial notation $n$ !! represents the product of all the even integers from 2 to $n$. For example, $8 ! !=2 \cdot 4 \cdot 6 \cdot 8$. What is the units digit of the following sum?
        $2 ! !+4 ! !+6 ! !+\cdots+2018 ! !+2020 ! !+2022 ! !$
        (A) 0
        (B) 2
        (C) 4
        (D) 6
        (E) 8
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_18(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_18',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The midpoints of the four sides of a rectangle are $(-3,0),(2,0),(5,4)$, and $(0,4)$. What is the area of the rectangle?
        (A) 20
        (B) 25
        (C) 40
        (D) 50
        (E) 80
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_19(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_19',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Mr. Ramos gave a test to his class of 20 students. The dot plot below shows the distribution of test scores.
        <img src="https://latex.artofproblemsolving.com/8/f/1/8f168ff6d1e7635e68e0139420bed9ecfc2e4993.png">
        Later Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students 5 extra points, which increased the median test score to 85 . What is the minimum number of students who received extra points?
        (Note that the median test score equals the average of the 2 scores in the middle if the 20 test scores are arranged in increasing order.)
        (A) 2
        (B) 3
        (C) 4
        (D) 5
        (E) 6

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_20(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_20',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number $x$ in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of $x$ ?
        <img src="https://latex.artofproblemsolving.com/8/1/4/814e3a8ce1c3c82c9dc6e97078dc7dbfcc954b3e.png">
        (A) $-1$
        (B) 5
        (C) 6
        (D) 8
        (E) 9
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_21(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_21',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Steph scored 15 baskets out of 20 attempts in the first half of a game, and 10 baskets out of 10 attempts in the second half. Candace took 12 attempts in the first half and 18 attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surprisingly they ended with the same overall percentage of baskets scored. How many more baskets did Candace score in the second half than in the first?
        <img src="https://latex.artofproblemsolving.com/4/2/a/42aefbe42671b2aeb0b90d88e171e5e03a00b73e.png">
        (A) 7
        (B) 8
        (C) 9
        (D) 10
        (E) 11
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_22(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_22',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A bus takes 2 minutes to drive from one stop to the next, and waits 1 minute at each stop to let passengers board. Zia takes 5 minutes to walk from one bus stop to the next. As Zia reaches a bus stop, if the bus is at the previous stop or has already left the previous stop, then she will wait for the bus. Otherwise she will start walking toward the next stop. Suppose the bus and Zia start at the same time toward the library, with the bus 3 stops behind. After how many minutes will Zia board the bus?
        <img src="https://wiki-images.artofproblemsolving.com//5/57/2022_AMC_8_Problem_22_Diagram.png">
        (A) 17
        (B) 19
        (C) 20
        (D) 21
        (E) 23
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_23(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_23',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A $\triangle$ or $\bigcirc$ is placed in each of the nine squares in a 3 -by- 3 grid. Shown below is a sample configuration with three $\Delta s$ in a line.
        How many configurations will have three $\triangle$s in a line and three $\bigcirc$ s in a line?
        <img src="https://latex.artofproblemsolving.com/f/7/9/f79f74a5bed66611fe027a9dd5ab0948b3a033ac.png">
        (A) 39
        (B) 42
        (C) 78
        (D) 84
        (E) 96
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_24(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_24',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The figure below shows a polygon $A B C D E F G H$, consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that $A I=E F=8$ and $G I I=14$. What is the volume of the prism?
        <img src="https://latex.artofproblemsolving.com/8/c/0/8c0183579e57a39614f2c3be1824f286b6bf4b86.png">
        (A) 112
        (B) 128
        (C) 192
        (D) 240
        (E) 288
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2022_25(self):
        keywords = [
            'amc8',
            'amc 8',
            '2022_25',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A cricket randomly hops between 4 leaves, on each turn hopping to one of the other 3 leaves with equal probability. After 4 hops, what is the probability that the cricket has returned to the leaf where it started?
        <img src="https://wiki-images.artofproblemsolving.com//f/f0/2022_AMC_8_Problem_25_Picture.jpg">
        (A) $\displaystyle \frac{{2}}{{9}}$
        (B) $\displaystyle \frac{{19}}{{80}}$
        (C) $\displaystyle \frac{{20}}{{81}}$
        (D) $\displaystyle \frac{{1}}{{4}}$
        (E) $\displaystyle \frac{{7}}{{27}}$
        
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

#end 2022
    def get_question_2020_1(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_1',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need?
        (A) 6
        (B) 8
        (C) 12
        (D) 18
        (E) 24

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_2(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_2',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Four friends do yardwork for their neighbors over the weekend, earning $\$ 15, \$ 20, \$ 25$, and $\$ 40$, respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned $\$ 40$ give to the others?
        (A) $\$ 5$
        (B) $\$ 10$
        (C) $\$ 15$
        (D) $\$ 20$
        (E) $\$ 25$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_3(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_3',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Carrie has a rectangular garden that measures 6 feet by 8 feet. She plants the entire garden with strawberry plants. Carrie is able to plant 4 strawberry plants per square foot, and she harvests an average of 10 strawberries per plant. How many strawberries can she expect to harvest?
        (A) 560
        (B) 960
        (C) 1120
        (D) 1920
        (E) 3840

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_4(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_4',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon?
        <img src="https://latex.artofproblemsolving.com/3/8/1/381ea96ddcbeccb0522187fcd4a41c78bd9c8364.png">
        (A) 35
        (B) 37
        (C) 39
        (D) 43
        (E) 49
        
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_5(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_5',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 5 cups. What percent of the total capacity of the pitcher did each cup receive?
        (A) 5
        (B) 10
        (C) 15
        (D) 20
        (E) 25

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_6(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_6',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Problem 6 directly behind Sharon. Darren sat in one of the cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car?
        (A) Aaron
        (B) Darren
        (C) Karen
        (D) Maren
        (E) Sharon
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_7(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_7',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        How many integers between 2020 and 2400 have four distinct digits arranged in increasing order? (For example, 2347 is one integer.)
        (A) 9
        (B) 10
        (C) 15
        (D) 21
        (E) 28

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_8(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_8',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Ricardo has 2020 coins, some of which are pennies (1-cent coins) and the rest of which are nickels (5-cent coins). He has at least one penny and at least one nickel. What is the difference in cents between the greatest possible and least possible amounts of money that Ricardo can have?
        (A) 8062
        (B) 8068
        (C) 8072
        (D) 8076
        (E) 8082


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_9(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_9',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Akash's birthday cake is in the form of a $4 \times 4 \times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into 64 smaller cubes, each measuring $1 \times 1 \times 1$ inch, as shown below. How many small pieces will have icing on exactly two sides?
        <img src="https://latex.artofproblemsolving.com/1/3/5/13575720613929277699552cc394543fb9d0346b.png">
        (A) 12
        (B) 16
        (C) 18
        (D) 20
        (E) 24

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_10(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_10',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Zara has a collection of 4 marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this?
        (A) 6
        (B) 8
        (C) 12
        (D) 18
        (E) 24
        
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_11(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_11',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/8/6/9/869acf55e021604fd3829ae77107a07511f6945f.png">
        After school, Maya and Naomi headed to the beach, 6 miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds?
        (A) 6
        (B) 12
        (C) 18
        (D) 20
        (E) 24
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_12(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_12',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        For a positive integer $n$, the factorial notation $n !$ represents the product of the integers from $n$ to 1 . (For example, $6 !=6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$.) What value of $N$ satisfies the following equation?
        $5 ! \cdot 9 !=12 \cdot N !$
        (A) 10
        (B) 11
        (C) 12
        (D) 13
        (E) 14
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_13(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_13',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Jamal has a drawer containing 6 green socks, 18 purple socks, and 12 orange socks. After adding more purple socks, Jamal noticed that there is now a $60 \%$ chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add?
        (A) 6
        (B) 9
        (C) 12
        (D) 18
        (E) 24
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_14(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_14',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/a/b/f/abffd65d59aacaaf81b6039c162d0898cca8b729.png">
        There are 20 cities in the County of Newton. Their populations are shown in the bar chart below. The average population of all the cities is indicated by the horizontal dashed line. Which of the following is closest to the total population of all 20 cities?
        (A) 65,000
        (B) 75,000
        (C) 85,000
        (D) 95,000
        (E) 105,000
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_15(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_15',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Suppose $15 \%$ of $x$ equals $20 \%$ of $y$. What percentage of $x$ is $y$ ?
        (A) 5
        (B) 35
        (C) 75
        (D) $133 \frac{{1}}{{3}}$
        (E) 300
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_16(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_16',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/9/f/1/9f1f0f8c2be3a35542af7640459f9a938b659c27.png">
        Each of the points $A, B, C, D, E$, and $F$ in the figure below represents a different digit from 1 to 6 . Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is 47 . What is the digit represented by B?
        (A) 1
        (B) 2
        (C) 3
        (D) 4
        (E) 5


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_17(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_17',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        How many factors of 2020 have more than 3 factors? (As an example, 12 has 6 factors, namely $1,2,3,4,6$, and 12 .)
        (A) 6
        (B) 7
        (C) 8
        (D) 9
        (E) 10
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_18(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_18',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/1/5/f/15fcfb06af407c88283742b188e91074fb48b60a.png">
        Rectangle $A B C D$ is inscribed in a semicircle with diameter $\overline{{F E}}$, as shown in the figure. Let $D A=16$, and let $F D=A E=9$. What is the area of $A B C D$ ?
        (A) 240
        (B) 248
        (C) 256
        (D) 264
        (E) 272

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_19(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_19',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by 15 ?
        (A) 3
        (B) 4
        (C) 5
        (D) 6
        (E) 8

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_20(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_20',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/f/7/0/f706bfa6f4339d99d594acb5159f6140c8eb1bb9.png">
        A scientist walking through a forest recorded as integers the heights of 5 trees standing in a row. She observed that each tree was either twice as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes are shown below, with blanks indicating the missing numbers. Based on her observations, the scientist was able to reconstruct the lost data. What was the average height of the trees, in meters?
        (A) 22.2
        (B) 24.2
        (C) 33.2
        (D) 35.2
        (E) 37.2
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_21(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_21',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/3/6/2/3626126e77aef045aa58c34a5af6adc480e57f17.png">
        A game board consists of 64 squares that alternate in color between black and white. The figure below shows square $P$ in the bottom row and square $Q$ in the top row. A marker is placed at $P$. A step consists of moving the marker onto one of the adjoining white squares in the row above. How many 7 -step paths are there from $P$ to $Q$ ? (The figure shows a sample path.)
        (A) 28
        (B) 30
        (C) 32
        (D) 33
        (E) 35
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_22(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_22',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown below.
        <img src="https://latex.artofproblemsolving.com/6/4/0/640f84b97add51c20f2c5af092b282884530e77b.png">
        For example, starting with an input of $N=7$, the machine will output $3 \cdot 7+1=22$. Then if the output is repeatedly inserted into the machine five more times, the final output is $26 .$
        $7 \rightarrow 22 \rightarrow 11 \rightarrow 34 \rightarrow 17 \rightarrow 52 \rightarrow 26$
        When the same 6-step process is applied to a different starting value of $N$, the final output is 1 . What is the sum of all such integers $N$ ?
        $N \rightarrow \_\_ \rightarrow \_\_ \rightarrow \_\_ \rightarrow \_\_ \rightarrow \_\_ \rightarrow 1$
        (A) 73
        (B) 74
        (C) 75
        (D) 82
        (E) 83
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_23(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_23',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Five different awards are to be given to three students. Each student will receive at least one award. In how many different ways can the awards be distributed?
        (A) 120
        (B) 150
        (C) 180
        (D) 210
        (E) 240
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_24(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_24',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/c/0/d/c0d420afb8c2f467480a85d6c02e403e50af81a8.png">
        A large square region is paved with $n^2$ gray square tiles, each measuring $s$ inches on a side. A border $d$ inches wide surrounds each tile. The figure below shows the case for $n=3$. When $n=24$, the 576 gray tiles cover $64 \%$ of the area of the large square region. What is the ratio $\frac{{d}}{{s}}$ for this larger value of $n ?$
        (A) $\displaystyle \frac{{6}}{{25}}$

        (B) $\displaystyle \frac{{1}}{{4}}$

        (C) $\displaystyle \frac{{9}}{{25}}$

        (D) $\displaystyle \frac{{7}}{{16}}$

        (E) $\displaystyle \frac{{9}}{{16}}$


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2020_25(self):
        keywords = [
            'amc8',
            'amc 8',
            '2020_25',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/a/5/5/a55c518a1179d67520c6a03827b4ba25ca1413f2.png">
        Rectangles $R_1$ and $R_2$, and squares $S_1, S_2$, and $S_3$, shown below, combine to form a rectangle that is 3322 units wide and 2020 units high. What is the side length of $S_2$ in units?
        (A) 651
        (B) 655
        (C) 656
        (D) 662
        (E) 666
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

#end 2020
    def get_question_2018_1(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_1',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        An amusement park has a collection of scale models, with ratio $1: 20$, of buildings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica to the nearest whole number?
        (A) 14
        (B) 15
        (C) 16
        (D) 18
        (E) 20

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_2(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_2',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        What is the value of the product
        $\displaystyle \left(1+\frac{{1}}{{1}}\right) \cdot\left(1+\frac{{1}}{{2}}\right) \cdot\left(1+\frac{{1}}{{3}}\right) \cdot\left(1+\frac{{1}}{{4}}\right) \cdot\left(1+\frac{{1}}{{5}}\right) \cdot\left(1+\frac{{1}}{{6}}\right) ?$
        (A) $\frac{{7}}{{6}}$
        (B) $\frac{{4}}{{3}}$
        (C) $\frac{{7}}{{2}}$
        (D) 7
        (E) 8


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_3(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_3',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle?
        (A) Arn
        (B) Bob
        (C) Cyd
        (D) Dan
        (E) Eve
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_4(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_4',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/f/4/d/f4d92072ddf7f5314e710dc9641eb84c3ea32879.png">
        The twelve-sided figure shown has been drawn on $1 \mathrm{{~cm}} \times 1 \mathrm{{~cm}}$ graph paper. What is the area of the figure in $\mathrm{{cm}}{{ }}^2$ ?
        (A) 12
        (B) $12.5$
        (C) 13
        (D) $13.5$
        (E) 14


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_5(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_5',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        What is the value of $1+3+5+\cdots+2017+2019-2-4-6-\cdots-2016-2018 ?$
        (A) $-1010$
        (B) $-1009$
        (C) 1008
        (D) 1009


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_6(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_6',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent 30 minutes driving on the coastal road, how many minutes did his entire trip take?
        (A) 50
        (B) 70
        (C) 80
        (D) 90
        (E) 100

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_7(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_7',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The 5 -digit number $\underline{{2}} \underline{{0}} \underline{{1}} \underline{{8}} \underline{{U}}$ is divisible by 9 . What is the remainder when this number is divided by 8 ?
        (A) 1
        (B) 3
        (C) 5
        (D) 6
        (E) 7

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_8(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_8',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students.
        <img src="https://latex.artofproblemsolving.com/f/7/a/f7add6258fd09de75421fb0d08e39071b65b128c.png">
        What was the mean number of days of exercise last week, rounded to the nearest hundredth, reported by the students in Mr. Garcia's class?
        (A) $3.50$
        (B) $3.57$
        (C) $4.36$
        (D) $4.50$
        (E) $5.00$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_9(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_9',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Jenica is tiling the floor of her 12 foot by 16 foot living room. She plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will she use?
        (A) 48
        (B) 87
        (C) 91
        (D) 96
        (E) 120

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_10(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_10',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        
        The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1,2 and 4 ?
        
        (A) $\displaystyle \frac{{3}}{{7}}$
        
        (B) $\displaystyle \frac{{7}}{{12}}$
        
        (C) $\displaystyle \frac{{12}}{{7}}$
        
        (D) $\displaystyle \frac{{7}}{{4}}$
        
        (E) $\displaystyle \frac{{7}}{{3}}$
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_11(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_11',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/b/a/6/ba6415e404832f3ef2afc016acabd151270a56ee.png">
        Abby, Bridget, and four of their classmates will be seated in two rows of three for a group picture, as shown.
        If the seating positions are assigned randomly, what is the probability that Abby and Bridget are adjacent to each other in the same row or the same column?
        (A) $\displaystyle \frac{{1}}{{3}}$
        (B) $\displaystyle \frac{{2}}{{5}}$
        (C) $\displaystyle \frac{{7}}{{15}}$
        (D) $\displaystyle \frac{{1}}{{2}}$ 
        (E) $\displaystyle \frac{{2}}{{3}}$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_12(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_12',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says $12: 30$ and his car clock says $12: 35$. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time?
        (A) $5: 50$
        (B) $6: 00$
        (C) $6: 30$
        (D) $6: 55$
        (E) $8: 10$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_13(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_13',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Laila took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between 0 and 100 , inclusive. Laila received the same score on the first four tests, and she received a higher score on the last test. Her average score on the five tests was 82 . How many values are possible for Laila's score on the last test?
        (A) 4
        (B) 5
        (C) 9
        (D) 10
        (E) 18

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_14(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_14',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Let $N$ be the greatest five-digit number whose digits have a product of 120 . What is the sum of the digits of $N$ ?
        (A) 15
        (B) 16
        (C) 17
        (D) 18
        (E) 20
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_15(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_15',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of 1 square unit, then what is the area of the shaded region, in square units?
        <img src="https://latex.artofproblemsolving.com/1/8/1/1814b98003d8f9d763c70aa6a56a765673f27d59.png">
        (A) $\displaystyle\frac{{1}}{{4}}$
        (B) $\displaystyle\frac{{1}}{{3}}$
        (C) $\displaystyle\frac{{1}}{{2}}$
        (D) 1
        (E) $\displaystyle\frac{{\pi}}{{2}}$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_16(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_16',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together?
        (A) 1440
        (B) 2880
        (C) 5760
        (D) 182,440
        (E) 362,880


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_17(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_17',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides 5 times as fast as Bella walks. The distance between their houses is 2 miles, which is 10,560 feet, and Bella covers $2 \frac{{1}}{{2}}$ feet with each step. How many steps will Bella take by the time she meets Ella?
        (A) 704
        (B) 845
        (C) 1056
        (D) 1760
        (E) 3520
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_18(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_18',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        How many positive factors does 23,232 have?
        (A) 9
        (B) 12
        (C) 28
        (D) 36
        (E) 42

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_19(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_19',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        
        <img src="https://latex.artofproblemsolving.com/f/5/9/f59b1af815a0ba23baf250a48b1029ee9d1bd5e4.png">
        In a sign pyramid a cell gets a " $+$ " if the two cells below it have the same sign, and it gets a "-" if the two cells below it have different signs. The diagram below illustrates a sign pyramid with four levels. How many possible ways are there to fill the four cells in the bottom row to produce a "+" at the top of the pyramid?
        (A) 2
        (B) 4
        (C) 8
        (D) 12
        (E) 16

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_20(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_20',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/0/5/7/0571cfd5e8f21ce8031af38df8ba2295bdf2449a.png">
        In $\triangle A B C$, a point $E$ is on $\overline{{A B}}$ with $A E=1$ and $E B=2$. Point $D$ is on $\overline{{A C}}$ so that $\overline{{D E}} \| \overline{{B C}}$ and point $F$ is on $\overline{{B C}}$ so that $\overline{{E F}} \| \overline{{A C}}$. What is the ratio of the area of $C D E F$ to the area of $\triangle A B C$ ?
        (A) $\displaystyle \frac{{4}}{{9}}$
        (B) $\displaystyle \frac{{1}}{{2}}$
        (C) $\displaystyle \frac{{5}}{{9}}$
        (D) $\displaystyle \frac{{3}}{{5}}$
        (E) $\displaystyle \frac{{2}}{{3}}$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_21(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_21',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        How many positive three-digit integers have a remainder of 2 when divided by 6 , a remainder of 5 when divided by 9 , and a remainder of 7 when divided by 11 ?
        (A) 1
        (B) 2
        (C) 3
        (D) 4
        (E) 5
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_22(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_22',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/7/c/1/7c13c3d233bfe4e1b9a7ecd2e6343fe5b8aa2e3a.png">
        Point $E$ is the midpoint of side $\overline{{C D}}$ in square $A B C D$, and $\overline{{B E}}$ meets diagonal $\overline{{A C}}$ at $F$. The area of quadrilateral $A F E D$ is 45 . What is the area of $A B C D$ ?
        (A) 100
        (B) 108
        (C) 120
        (D) 135
        (E) 144

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_23(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_23',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/5/4/d/54d911c096b9c5403a914f8b8c2b05b4915494f1.png">
        From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon?
        (A) $\displaystyle \frac{{2}}{{7}}$
        (B) $\displaystyle \frac{{5}}{{42}}$
        (C) $\displaystyle \frac{{11}}{{14}}$
        (D) $\displaystyle \frac{{5}}{{7}}$
        (E) $\displaystyle \frac{{6}}{{7}}$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_24(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_24',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/a/1/d/a1d819cf8339fd4ae7e3d612b459da3b1e8cdc7b.png">
        In the cube $A B C D E F G H$ with opposite vertices $C$ and $E, J$ and $I$ are the midpoints of edges $\overline{{F B}}$ and $\overline{{H D}}$, respectively. Let $R$ be the ratio of the area of the cross-section E.JCI to the area of one of the faces of the cube. What is $R^2$ ?
        (A) $\displaystyle \frac{{5}}{{4}}$
        (B) $\displaystyle \frac{{4}}{{3}}$
        (C) $\displaystyle \frac{{3}}{{2}}$
        (D) $\displaystyle \frac{{25}}{{16}}$
        (E) $\displaystyle \frac{{9}}{{4}}$


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2018_25(self):
        keywords = [
            'amc8',
            'amc 8',
            '2018_25',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        How many perfect cubes lie between $2^8+1$ and $2^{{18}}+1$, inclusive?
        (A) 4
        (B) 9
        (C) 10
        (D) 57
        (E) 58

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

#end 2018

    def get_question_2016_1(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_1',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The longest professional tennis match lasted a total of 11 hours and 5 minutes. How many minutes is that?
        (A) 605
        (B) 655
        (C) 665
        (D) 1005
        (E) 1105

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_2(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_2',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/b/5/d/b5d7e3f5ecfd57e90e56a341f52fc4b9b93b2457.png">
        In rectangle $A B C D, A B=6$ and $A D=8$. Point $M$ is the midpoint of $\overline{{A D}}$. What is the area of $\triangle A M C$ ?
        (A) 12
        (B) 15
        (C) 18
        (D) 20
        (E) 24


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_3(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_3',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Four students take an exam. Three of their scores are 70,80 , and 90 . If the average of their four scores is 70 , then what is the remaining score?
        (A) 40
        (B) 50
        (C) 55
        (D) 60
        (E) 70

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_4(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_4',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        When Cheenu was a boy he could run 15 miles in 3 hours and 30 minutes. As an old man he can now walk 10 miles in 4 hours. How many minutes longer does it take for him to travel a mile now compared to when he was a boy?
        (A) 6
        (B) 10
        (C) 15
        (D) 18
        (E) 30


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_5(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_5',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The number $N$ is a two-digit number.
        - When $N$ is divided by 9 , the remainder is $1 .$
        - When $N$ is divided by 10 , the remainder is $3 .$
        What is the remainder when $N$ is divided by 11 ?
        (A) 0
        (B) 2
        (C) 4
        (D) 5
        (E) 7


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_6(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_6',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names? frequency
        <img src="https://latex.artofproblemsolving.com/7/3/9/7396694d92e8f9794065daafaf571852434d0b08.png">
        (A) 3
        (B) 4
        (C) 5
        (D) 6
        (E) 7

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_7(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_7',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Which of the following numbers is not a perfect square?
        (A) $1^{{2016}}$
        (B) $2^{{2017}}$
        (C) $3^{{2018}}$
        (D) $4^{{2019}}$
        (E) $5^{{2020}}$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_8(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_8',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Find the value of the expression
        $100-98+96-94+92-90+\cdots+8-6+4-2$
        (A) 20
        (B) 40
        (C) 50
        (D) 80
        (E) 100


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_9(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_9',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        What is the sum of the distinct prime integer divisors of 2016 ?
        (A) 9
        (B) 12
        (C) 16
        (D) 49
        (E) 63

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_10(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_10',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        
        Suppose that $a * b$ means $3 a-b$. What is the value of $x$ if
        $2 *(5 * x)=1$
        (A) $\frac{{1}}{{10}}$
        (B) 2
        (C) $\frac{{10}}{{3}}$
        (D) 10
        (E) 14

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_11(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_11',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is 132 .
        (A) 5
        (B) 7
        (C) 9
        (D) 11
        (E) 12
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_12(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_12',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Jefferson Middle School has the same number of boys and girls. $\frac{{3}}{{4}}$ of the girls and $\frac{{2}}{{3}}$ of the boys went on a field trip. What fraction of the students on the field trip were girls?
        (A) $\frac{{1}}{{2}}$
        (B) $\frac{{9}}{{17}}$
        (C) $\frac{{7}}{{13}}$
        (D) $\frac{{2}}{{3}}$
        (E) $\frac{{14}}{{15}}$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_13(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_13',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Two different numbers are randomly selected from the set $\{{-2,-1,0,3,4,5\}}$ and multiplied together. What is the probability that the product is 0 ?
        (A) $\frac{{1}}{{6}}$
        (B) $\frac{{1}}{{5}}$
        (C) $\frac{{1}}{{4}}$
        (D) $\frac{{1}}{{3}}$
        (E) $\frac{{1}}{{2}}$


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_14(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_14',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Karl's car uses a gallon of gas every 35 miles, and his gas tank holds 14 gallons when it is full. One day, Karl started with a full tank of gas, drove 350 miles, bought 8 gallons of gas, and continued driving to his destination. When he arrived, his gas tank was half full. How many miles did Karl drive that day?
        (A) 525
        (B) 560
        (C) 595
        (D) 665
        (E) 735
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_15(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_15',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        What is the largest power of 2 that is a divisor of $13^4-11^4$ ?
        (A) 8
        (B) 16
        (C) 32
        (D) 64
        (E) 128

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_16(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_16',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Annie and Bonnie are running laps around a 400-meter oval track. They started together, but Annie has pulled ahead because she runs $25 \%$ faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?
        (A) $1 \frac{{1}}{{4}}$
        (B) $3 \frac{{1}}{{3}}$
        (C) 4
        (D) 5
        (E) 25


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_17(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_17',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        An ATM password at Fred's Bank is composed of four digits from 0 to 9 , with repeated digits allowable. If no password may begin with the sequence $9,1,1$, then how many passwords are possible?
        (A) 30
        (B) 7290
        (C) 9000
        (D) 9990
        (E) 9999

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_18(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_18',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        In an All-Area track meet, 216 sprinters enter a 100 - meter dash competition. The track has 6 lanes, so only 6 sprinters can compete at a time. At the end of each race, the five non-winners are eliminated, and the winner will compete again in a later race. How many races are needed to determine the champion sprinter?
        (A) 36
        (B) 42
        (C) 43
        (D) 60
        (E) 72


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_19(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_19',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        
        The sum of 25 consecutive even integers is 10,000 . What is the largest of these 25 consecutive integers?
        (A) 360
        (B) 388
        (C) 412
        (D) 416
        (E) 424


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_20(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_20',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The least common multiple of $a$ and $b$ is 12 , and the least common multiple of $b$ and $c$ is 15 . What is the least possible value of the least common multiple of $a$ and $c$ ?
        (A) 20
        (B) 30
        (C) 60
        (D) 120
        (E) 180

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_21(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_21',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A top hat contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn?
        (A) $\frac{{3}}{{10}}$
        (B) $\frac{{2}}{{5}}$
        (C) $\frac{{1}}{{2}}$
        (D) $\frac{{3}}{{5}}$
        (E) $\frac{{7}}{{10}}$
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_22(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_22',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/7/c/1/7c13c3d233bfe4e1b9a7ecd2e6343fe5b8aa2e3a.png">
        Rectangle $D E F A$ below is a $3 \times 4$ rectangle with $D C=C B=B A=1$ The area of the "bat wings" (shaded area) is
        (A) 2
        (B) $2 \frac{{1}}{{2}}$
        (C) 3
        (D) $3 \frac{{1}}{{2}}$
        (E) 4

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_23(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_23',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Two congruent circles centered at points $A$ and $B$ each pass through the other circle's center. The line containing both $A$ and $B$ is extended to intersect the circles at points $C$ and $D$. The circles intersect at two points, one of which is $E$. What is the degree measure of $\angle C E D$ ?
        (A) 90
        (B) 105
        (C) 120
        (D) 135
        (E) 150

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_24(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_24',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The digits $1,2,3,4$, and 5 are each used once to write a five-digit number $P Q R S T$. The three-digit number $P Q R$ is divisible by 4 , the three-digit number $Q R S$ is divisible by 5 , and the three-digit number $R S T$ is divisible by 3 . What is $P$ ?
        (A) 1
        (B) 2
        (C) 3
        (D) 4
        (E) 5
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2016_25(self):
        keywords = [
            'amc8',
            'amc 8',
            '2016_25',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A semicircle is inscribed in an isosceles triangle with base 16 and height 15 so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?
        <img src="https://latex.artofproblemsolving.com/5/8/5/585fca3c7a910c5787429738a441c0c2accc394d.png">
        (A) $4 \sqrt{{3}}$
        (B) $\frac{{120}}{{17}}$
        (C) 10
        (D) $\frac{{17 \sqrt{{2}}}}{{2}}$
        (E) $\frac{{17 \sqrt{{3}}}}{{2}}$


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

#end 2016

    def get_question_2014_1(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_1',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Harry and Terry are each told to calculate $8-(2+5)$. Harry gets the correct answer. Terry ignores the parentheses and calculates $8-2+5$. If Harry's answer is $H$ and Terry's answer is $T$, what is $H-T$ ?
        (A) $-10$
        (B) $-6$
        (C) 0
        (D) 6 
        (E) 10


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_2(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_2',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25 -cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?
        (A) 1
        (B) 2
        (C) 3
        (D) 4
        (E) 5


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_3(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_3',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Isabella had a week to read a book for a school assignment. She read an average of 36 pages per day for the first three days and an average of 44 pages per day for the next three days. She then finished the book by reading 10 pages on the last day. How many pages were in the book?
        (A) 240
        (B) 250
        (C) 260
        (D) 270
        (E) 280

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_4(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_4',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The sum of two prime numbers is 85 . What is the product of these two prime numbers?
        (A) 85
        (B) 91
        (C) 115
        (D) 133
        (E) 166


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_5(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_5',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Margie's car can go 32 miles on a gallon of gas, and gas currently costs $\$$4 per gallon. How many miles can Margie drive on $\$$20?
        (A) 64
        (B) 128
        (C) 160
        (D) 320
        (E) 640



        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_6(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_6',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Six rectangles each with a common base width of 2 have lengths of $1,4,9,16,25$, and 36 . What is the sum of the areas of the six rectangles?
        (A) 91
        (B) 93
        (C) 162
        (D) 182
        (E) 202

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_7(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_7',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        There are four more girls than boys in Ms. Raub's class of 28 students. What is the ratio of number of girls to the number of boys in her class?
        (A) $3: 4$
        (B) $4: 3$
        (C) $3: 2$
        (D) $7: 4$
        (E) $2: 1$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_8(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_8',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Eleven members of the Middle School Math Club each paid the same integer amount for a guest speaker to talk about problem solving at their math club meeting. In all, they paid their guest speaker $\$ \underline{{1 A 2}}$. What is the missing digit $\mathrm{{A}}$ of this 3 -digit number?
        (A) 0
        (B) 1
        (C) 2
        (D) 3
        (E) 4


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_9(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_9',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        In $\triangle A B C, D$ is a point on side $\overline{{A C}}$ such that $B D=D C$ and $\angle B C D$ measures $70^{{\circ}}$. What is the degree measure of $\angle A D B$ ?
        <img src="https://latex.artofproblemsolving.com/9/4/7/94770df9a0e1d5a71f602bfb3b45022dcca9dec4.png">
        (A) 100
        (B) 120
        (C) 135
        (D) 140
        (E) 150

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_10(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_10',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        
        The first AMC 8 was given in 1985 and it has been given annually since that time. Samantha turned 12 years old the year that she took the seventh AMC 8. In what year was Samantha born?
        (A) 1979
        (B) 1980
        (C) 1981
        (D) 1982
        (E) 1983

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_11(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_11',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Jack wants to bike from his house to Jill's house, which is located three blocks east and two blocks north of Jack's house. After biking each block, Jack can continue either east or north, but he needs to avoid a dangerous intersection one block east and one block north of his house. In how many ways can he reach Jill's house by biking a total of five blocks?
        (A) 4
        (B) 5
        (C) 6
        (D) 8
        (E) 10

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_12(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_12',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures did not identify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random will match all three correctly as a fraction?
        (A) $\frac{{1}}{{9}}$
        (B) $\frac{{1}}{{6}}$
        (C) $\frac{{1}}{{4}}$
        (D) $\frac{{1}}{{3}}$
        (E) $\frac{{1}}{{2}}$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_13(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_13',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        If $n$ and $m$ are integers and $n^2+m^2$ is even, which of the following is impossible?
        (A) $n$ and $m$ are even
        (B) $n$ and $m$ are odd
        (C) $n+m$ is even
        (D) $n+m$ is odd
        (E) none of these are impossible

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_14(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_14',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Rectangle $A B C D$ and right triangle $D C E$ have the same area. They are joined to form a trapezoid, as shown. What is $D E$ ?
        <img src="https://latex.artofproblemsolving.com/c/3/5/c358884777664e69762bbb69b74c260349626ff4.png">
        (A) 12
        (B) 13
        (C) 14
        (D) 15
        (E) 16
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_15(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_15',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        <img src="https://latex.artofproblemsolving.com/f/0/e/f0e953697ad3937a071ae08f39fe3a6cb0648811.png">
        The circumference of the circle with center $O$ is divided into 12 equal arcs, marked the letters $A$ through $L$ as seen below. What is the number of degrees in the sum of the angles $x$ and $y$ ?
        (A) 75
        (B) 80
        (C) 90
        (D) 120
        (E) 150


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_16(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_16',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The "Middle School Eight' basketball conference has 8 teams. Every season, each team plays every other conference team twice (home and away), and each team also plays 4 games against non-conference opponents. What is the total number of games in a season involving the "Middle School Eight' teams?
        (A) 60
        (B) 88
        (C) 96
        (D) 144
        (E) 160

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_17(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_17',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        George walks 1 mile to school. He leaves home at the same time each day, walks at a steady speed of 3 miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first $\frac{{1}}{{2}}$ mile at a speed of only 2 miles per hour. At how many miles per hour must George run the last $\frac{{1}}{{2}}$ mile in order to arrive just as school begins today?
        (A) 4
        (B) 6
        (C) 8
        (D) 10
        (E) 12


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_18(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_18',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely?
        (A) all 4 are boys 
        (B) all 4 are girls 
        (C) 2 are girls and 2 are boys 
        (D) 3 are of one gender and 1 is of the other gender 
        (E) all of these outcomes are equally likely

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_19(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_19',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        
        A cube with 3-inch edges is to be constructed from 27 smaller cubes with 1-inch edges. Twenty-one of the cubes are colored red and 6 are colored white. If the 3-inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?
        (A) $\frac{{5}}{{54}}$
        (B) $\frac{{1}}{{9}}$
        (C) $\frac{{5}}{{27}}$
        (D) $\frac{{2}}{{9}}$
        (E) $\frac{{1}}{{3}}$


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_20(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_20',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Rectangle $A B C D$ has sides $C D=3$ and $D A=5$. A circle with a radius of 1 is centered at $A$, a circle with a radius of 2 is centered at $B$, and a circle with a radius of 3 is centered at $C$. Which of the following is closest to the area of the region inside the rectangle but outside all three circles?
        <img src="https://latex.artofproblemsolving.com/0/a/5/0a5cf23036c6f8baa2e09775cc716c2ef6913400.png">
        (A) $3.5$
        (B) $4.0$
        (C) $4.5$
        (D) $5.0$
        (E) $5.5$

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_21(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_21',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        The 7-digit numbers $\underline{{74 A 52 B 1}}$ and $\underline{{326 A B 4 C}}$ are each multiples of 3 . Which of the following could be the value of $C$ ?
        (A) 1
        (B) 2
        (C) 3
        (D) 5
        (E) 8


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_22(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_22',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A 2-digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number?
        (A) 1
        (B) 3
        (C) 5
        (D) 7
        (E) 9
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_23(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_23',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        Three members of the Euclid Middle School girls' softball team had the following conversation.
        Ashley. I just realized that our uniform numbers are all 2-digit primes.
        Bethany: And the sum of your two uniform numbers is the date of my birthday earlier this month.
        Caitlin: That's funny. The sum of your two uniform numbers is the date of my birthday later this month.
        Ashley: And the sum of your two uniform numbers is today's date.
        What number does Caitlin wear?
        (A) 11
        (B) 13
        (C) 17
        (D) 19
        (E) 23

        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_24(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_24',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        One day the Beverage Barn sold 252 cans of soda to 100 customers, and every customer bought at least one can of soda. What is the maximum possible median number of cans of soda bought per customer on that day?
        (A) $2.5$
        (B) $3.0$
        (C) $3.5$
        (D) $4.0$
        (E) $4.5$
        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

    def get_question_2014_25(self):
        keywords = [
            'amc8',
            'amc 8',
            '2014_25',
            ]
        
        
        hint_s = rf"""
        <b>See the following managers for more detailed explanation:</b>
        
        
        """
        
        prob_s = rf"""
        A straight one-mile stretch of highway, 40 feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at 5 miles per hour, how many hours will it take to cover the one-mile stretch?
        <img src="https://latex.artofproblemsolving.com/3/9/5/395870fbc2c4f6e6f0bd6d9ebca32f7558124b1b.png">
        Note: 1 mile $=5280$ feet
        (A) $\frac{{\pi}}{{11}}$
        (B) $\frac{{\pi}}{{10}}$
        (C) $\frac{{\pi}}{{5}}$
        (D) $\frac{{2 \pi}}{{5}}$
        (E) $\frac{{2 \pi}}{{3}}$


        """
        
        soln_s = rf"""
        
        """
        
        answer_s = rf"""
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass

#end 2014

    def get_question_SAMPLE(self):
        keywords = [
            'amc8',
            'amc 8',
            ]
        
        hint_s = rf"""
        <b>:</b>
        
        """
        
        prob_s = rf"""

        """
        
        soln_s = rf"""

        
        {hint_s.strip()}

        """
        
        answer_s = rf"""
        
        
        """

        result = {
            'keywords': keywords,
            'prob_s': prob_s.strip(),
            'soln_s': soln_s.strip(),
            'answer_s': answer_s.strip(),
            }
        return result
        pass
 
    pass
#class Amc8StoredQuestions:
