24 game solver: every way to make 24

Enter four numbers and see every distinct way to reach 24 with + − × ÷ and brackets, or a plain "no solution" when there is none. Change the target if you play a variant.

How it works, and what counts as different

The solver tries every way of pairing the numbers with the four operations and every bracketing, using exact fractions (never rounded decimals), so a result of 24 is exactly 24. Answers that are the same up to swapping the two sides of a + or × (3 + 5 and 5 + 3) count once. Up to 12 are shown, the ones that stay in whole numbers first. The classic example is 3, 3, 8, 8: the only way is 8 ÷ (3 − 8 ÷ 3), which passes through the fraction 1/3, so many people give up on it. Cards with a face value usually count as 1 (ace) and 11 to 13, so just type the number.

This page uses the "all numbers, exactly once" rule of the 24 game. The Countdown numbers round is different: you may leave numbers unused, and fractions are not allowed. For that game, use the Countdown numbers solver, or play the daily Parsum board, where every target has an exactly computed fewest-step par.