24 Game Solver — Find All Ways to Make 24

Standard deck: 1 (Ace) through 13 (King). Any positive integer up to 99 works.
(default 24)
Try one
More puzzles
3
+
5
×
2
+
1
= 24

Enter 4 numbers to solve

Find all ways to make 24 (or any target) using +, −, ×, ÷ with step-by-step breakdowns.

What is the 24 Game?

The 24 Game (also called the 24 Card Game or Make 24) is a classic mathematical puzzle invented by Robert Sun in 1988. Four numbers are drawn from a standard playing card deck (Ace = 1 through King = 13), and the goal is to combine all four using addition (+), subtraction (−), multiplication (×), and division (÷) to get exactly 24.

Each number must be used exactly once. Parentheses can change the order of operations. The game is widely used in classrooms to develop mental math, number sense, and algebraic thinking.

Use all 4 numbers

Every number must be used exactly once. You cannot skip or repeat any number.

4 operations only

Addition, subtraction, multiplication, and division. No exponents or other operations.

Parentheses allowed

Use parentheses freely to change the order of operations and group calculations.

Result must be 24

The final answer after all operations must equal exactly 24 (or your custom target).

Strategies to solve faster

  1. Look for factor pairs of 24.  24 = 1×24, 2×12, 3×8, 4×6. Try to make one factor from two numbers and the other from the remaining two.
  2. Try addition / subtraction chains.  If factor pairs don't work, combine three numbers with multiplication and adjust the fourth with addition or subtraction.
  3. Don't forget division.  The hardest puzzles often need division. The classic 3,3,8,8 requires 8 ÷ (3 − 8 ÷ 3) = 24.
  4. Use this solver to check.  Enter your 4 numbers above and click Find solutions — every possible answer with step-by-step breakdowns.

Frequently asked

The 24 Game is a mathematical card game where players use four numbers and basic arithmetic operations (+, −, ×, ÷) to make exactly 24. Each number must be used exactly once. Parentheses change the order of operations. Invented by Robert Sun in 1988 and widely used in schools to develop mental math.
First look for factor pairs of 24 (3×8, 4×6, 2×12) — try to make one factor from two numbers and the other from the remaining two. If that fails, try chains of operations. Common targets: 8×3, 6×4, 24×1.
No. 1,1,1,1 for example has no solution. With numbers 1–9 about 80% of four-number combinations are solvable. The hardest commonly cited is 3,3,8,8 requiring 8 ÷ (3 − 8 ÷ 3) = 24.
The hardest puzzles typically have only one solution and require division or complex nesting. Famous examples: 3,3,8,8 and 1,5,5,5. Our solver rates difficulty by solution count: Expert (1–2), Hard (3–5), Medium (6–12), Easy (13+).
Yes — it's excellent for mental math, number sense, and arithmetic fluency. It teaches order of operations, creative problem-solving, and strategic thinking. Many teachers use it as a classroom warm-up.
Some four-number combinations from 1–9 cannot make 24, such as 1,1,1,1 and 1,1,1,2. With cards 1–13, about 458 of the 715 possible combinations are solvable. Our solver tells you instantly.