24 Game Solver
Enter your numbers and see every way to make 24.
Allow fraction steps like 8 ÷ (3 − 8 ÷ 3)
Tip: you can paste "3 5 8 1", "3,5,8,1" or "3581".
Solutions
Enter your numbers and press Solve to see the results here.
How the 24 game works
You get a hand of numbers — four in the classic card game, each between 1 (ace) and 13 (king). Use every number exactly once, combine them with addition, subtraction, multiplication and division, and group with parentheses to control the order. Reach exactly 24 and the hand is solved.
Some hands only work through a fraction step — 3, 3, 8, 8 famously needs 8 ÷ (3 − 8 ÷ 3). Switch "Fraction steps" on above to allow non-integer intermediate results, or leave it off for classic whole-number rules. With three or five numbers the same rule applies: use each number once and land on 24.
Classic hands, answered
The most-searched 24 game hands, solved. Tap one in the example chips above to load it into the solver and browse every alternative.
4 4 10 10
(10 × 10 − 4) ÷ 4 = 24. The most famous hard hand: 10 × 10 makes 100, minus 4 is 96, and 96 ÷ 4 lands exactly on 24.
3 3 8 8
8 ÷ (3 − 8 ÷ 3) = 24. No whole-number solution exists — 8 ÷ 3 leaves 1/3 inside the parentheses, and 8 ÷ 1/3 is 24.
1 5 5 5
5 × (5 − 1 ÷ 5) = 24. Another fraction key: 1 ÷ 5 trims the second 5 to 4.8, and 5 × 4.8 is exactly 24.
Solver FAQ
Can a hand be unsolvable?
Yes — plenty of hands have no solution. 1, 1, 1, 1 is the extreme case: no arrangement of ones can reach 24. When this solver answers "No solution" it has checked every permutation, every operation order and every parenthesization, so the verdict is final. Deal yourself another hand.
Which operations are allowed?
Addition, subtraction, multiplication and division, grouped with parentheses. No exponents, square roots, concatenation or factorials, and every number must be used exactly once — those are the classic rules and the ones this solver applies.
Are fraction steps allowed?
With "Fraction steps" on, intermediate results may be fractions — 8 ÷ 3 = 8/3 is fine as long as the final result is exactly 24. Turn it off to enforce whole numbers at every step, the stricter classic variant.