Twenty-four Game

24 Game

Basic goal of 24 game is to manipulate four cards so that the end result is 24. For example: [11, 8, 3, 5] will be (11-9)*(3+5) = 24. Since original version of 24 is player with ordinary deck of playing cards. Therefore, the integer will be from 1 to 13.

Reference: 24 Game

• Number: from 1 to 13
• Operator:
  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Parentheses

Thoughts

First thought of solve this problem will be using brute-force. For number can be only used once, there are 4^4 = 256 ways to pick cards. We can only use 3 operators between 4 numbers. There are 4^3 = 56 ways, if we don’t count parentheses yet. There are 5 ways to add parentheses:

• ((AB)C)D
• (A(BC))D
• (AB)(CD)
• A((BC)D)
• A(B(CD))

Therefore, we have a total of 4^4 * 4^3 * 5 = 81,920 ways to place our numbers and operators.