24 Game Calculator

Understanding the 24 Game

What is the 24 Game?

The 24 Game is a mathematical card game where the objective is to find a way to manipulate four numbers to get the result of 24. These four numbers are typically single digits from 1 to 9.

Rules of the 24 Game

• Use each of the four numbers exactly once
• Use only basic arithmetic operations: addition (+), subtraction (-), multiplication (×), and division (÷)
• The final result must equal 24
• Parentheses can be used to change the order of operations

Mathematical Representation

The general form of a 24 Game solution can be represented as:

\[((a \circ b) \circ c) \circ d = 24\]

Where \(a\), \(b\), \(c\), and \(d\) are the four given numbers, and \(\circ\) represents one of the four basic arithmetic operations.

Example Calculation

Let's solve the 24 Game for the numbers 3, 3, 8, and 9:

1. A correct solution is: \((3 \times (3 + 8)) - 9 = 24\)
2. Step-by-step calculation:
   • \(3 + 8 = 11\)
   • \(3 \times 11 = 33\)
   • \(33 - 9 = 24\)
3. Verification: \(24 = 24\)

This example correctly results in 24, demonstrating a valid solution to the 24 Game.

Visual Representation

This diagram shows the four numbers (3, 3, 8, 9) used in the 24 game, the target number 24, and the correct solution.