Mathematical exploration: The game 24An exploration of the theoretical support of the game 24An introduction to the game 24:Overview:The game 24 is a mathematical card game that originated in China in the 1960s and later popularized in China and America. It's a game that requires its players to do quick calculations, and it can be competitive. After years of distribution and development, the game has come in many different rules. In this research paper, the topic mainly focuses on the original rule. Rules: In game 24, players use a standard deck of cards where jokers are eliminated from the deck of cards. By randomly selecting 4 cards from the 52-card deck, players must obtain a result of 24 using addition, subtraction, multiplication and division. In the game, cards 2 to 10 represent the numbers 2 to 10, A represents 1 and J, Q, K represent the numbers 11, 12, 13. Each card must be used and can only be used once. For example: A, A, 4, Q (1, 1, 4, 12) can be calculated as [4 - (1 + 1)] × 12 to get a result of 24. Generally, there are several ways to solve a There are, however, 24 game questions, but there are also questions with a single answer or unsolvable questions. Fraction Calculation: Usually in the game only whole numbers are used to get a result of 24. However, in some difficult questions in the game of 24, fraction calculation is required. . For example: 2, 5, 5, 10 can be calculated as follows: (5 − 2 ÷ 10) × 5, or 24 over 5 multiplied by 5. Rationale: The reasons for 24 are chosen as the result of the calculation: The reason for 24 is chosen as the result instead of other numbers because between 1 and 30, 24 has the most factors, 1, 2, 4, 6, 8, 12, 24. While other numbers such as 22, 23 or 17, 18...... middle of the sheet......, c, b, a)There are two ways in total to calculate the 3 steps: Let ⋇ represent +, -, ×, ÷1. [(a⋇b)⋇c]⋇d2. (a⋇b)⋇(c⋇d)By calculating the above 24 permutations and swapping ⋇ with +, -, ×, ÷, it is possible for a computer program to obtain and record all unsolvable combinations . According to the data, there are 458 unsolvable combinations out of a total of 1820 results. Therefore, the probability that a randomly chosen combination can be solved is ((1820-458))/1820 × 100%≈ 74.84%. However, the above result is only the theoretical result. Although in the game the colors do not matter, in a realistic calculation the color change must be taken into account. A study of the unsolvable question 4 cards 3 identical 1 different 2 identical 2 different 2 identical the other 2 identical 4 different Unsolvable questions in total 8 70 33 239 108 458