Make 40 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 40. 40 cannot be made with + - × ÷, concatenation, or decimals (the solver checked every expression) — solutions need square roots, factorials, or exponents.

Solutions using only + - × ÷

No expression made of four plain 9s and + - × ÷ reaches 40 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 40 either — every combination was checked.

Solutions with square roots, factorials, exponents

(9 + 9 × sqrt(9)) / .9 = 40
(9 - sqrt(9))! / (9 + 9) = 40
(9 / sqrt(9))!! / (9 + 9) = 40
(9 - sqrt(9)!)!! / (9 + 9) = 40
(9 / (.9 + .9))! / sqrt(9) = 40

…and 232 more at this tier.

237 distinct solutions found in total, after removing trivial rearrangements.

Make 39 with four 9s · Make 41 with four 9s

The Number Lab

Same idea, different constraints: four 9s, four 4s, or any four digits you like.

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Play the daily Four Nines puzzle, pick another number in the solver, or find more free math games.