Solver
Every way to make 24.
Put in four numbers and get all of them — each number used exactly once, with + − × ÷. The search is exhaustive and runs on exact fractions, so solutions that pass through thirds and sevenths are found too.
How the search works
It repeatedly takes an ordered pair of the numbers still on the table, applies one of the four operators, and recurses on what is left. Addition and multiplication are commutative, so mirrored pairs are skipped — that halves the work without losing a single distinct solution.
Everything is computed as exact rationals rather than decimals. That matters: 8 ÷ (3 − 8 ÷ 3) is exactly 24, but in floating point it lands a hair off and a naive solver throws it away.
Solutions are deduplicated by their fully parenthesised form, so (8 − 4) × (3 + 3) and (3 + 3) × (8 − 4) count once. Reorderings of the same expression are still listed separately when the bracketing genuinely differs.
Want to work it out yourself instead? Play a board.