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24 Game
The 24 Game is an arithmetic puzzle that became a popular classroom game after Robert Sun published a card version in 1988. You are given four numbers and must combine them with the four basic operations to reach exactly 24, training fast mental arithmetic and creative thinking.
24 Game Rules
Each round presents four numbers, traditionally from playing cards 1 through 9 (some versions go higher). Your task is to use all four numbers exactly once to make a total of exactly 24.
You may combine the numbers with addition, subtraction, multiplication, and division, and you can group operations with parentheses in any order. Every number must be used once and only once, and no number may be left out or reused.
The first player to find a valid expression equal to 24 calls it out and wins the round. If no combination of the four numbers can reach 24, the round is declared unsolvable and a new set is drawn.
24 Game Strategy & Tips
Hunt for factor pairs
Twenty-four breaks down as 4×6, 3×8, 2×12, and 1×24. Scan your four numbers for any pair you can turn into one of these, then build the matching factor from the other two.
Use division to shrink big numbers
When a number is too large, divide it down. For example with 8, 8, 3, 3 you can compute 8 ÷ (3 − 8 ÷ 3) — division and subtraction reshape awkward values into useful ones.
Try the 'make 1' trick
Turning two numbers into 1 (like 7 ÷ 7 or 5 − 4) lets you multiply 24 by 1 harmlessly, freeing the remaining two numbers to build 24 on their own.
Don't forget subtraction paths
Many solutions come from a difference, such as (numbers that make 30) minus (numbers that make 6). When multiplication stalls, look for two groups whose difference is 24.
Frequently Asked Questions
Do you have to use all four numbers?
Yes. Every one of the four numbers must be used exactly once, and the operations and parentheses are up to you, but no number can be skipped or repeated.
Which operations are allowed?
The four basic operations: addition, subtraction, multiplication, and division. Parentheses are allowed to control the order, but exponents and roots are not in the standard game.
Is every set of four numbers solvable?
No. Some combinations cannot reach 24 by any arrangement. When a card has no solution it is simply set aside and a new one is played.
Are there always whole numbers in the middle?
Not necessarily. Intermediate results can be fractions, as in 8 ÷ (3 − 8 ÷ 3) = 24, so don't dismiss division just because it produces a fraction.