Mathematical Exploration: Game 24An Exploration of the Theoretical Support of Game 24An Introduction to Game 24:Overview:Game 24 is a mathematical card game originating in China in the 60s and later popularized in China and America. It's a game that requires players to do quick calculations and can be competitive. After years of popularization and development, the game has resulted from 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 2-10 represent the numbers 2-10, 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. In general, there are several ways to solve a problem Question of the game of 24, however there are also questions with a unique answer or unsolvable questions. Calculating Fractions: Usually only whole numbers are used in the game to get a result of 24. However, in some difficult Game of 24 questions, calculating fractions is required. . For example: 2, 5, 5, 10 can be calculated as (5 − 2 ÷ 10) × 5 which is 24 over 5 multiplied by 5. Reason: The reasons for 24 are chosen as the result of the calculation: The reason for 24 is chosen as a result of instead of other numbers because between 1 and 30, 24 has the most factors, 1, 2, 4, 6, 8, 12, 24. While other numbers like 22, 23 or 17, 18... ... half 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 24 permutations above and exchanging ⋇ 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 the total 1820 results. Therefore, the probability of a randomly chosen combination that can be solved is ((1820-458))/1820 × 100%≈ 74.84% However, the above result is only the theoretical result. Although suits do not count in the game, the change of suit must be taken into account in the realistic calculation. A study on the unsolvable question 4 cards 3 the same 1 different 2 the same 2 different 2 the same the other 2 the same 4 different Total unsolvable questions 8 70 33 239 108 458