Make 57 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 57. 57 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 57 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 57 either — every combination was checked.

Solutions with square roots, factorials, exponents

(9 + 9 / .9) × sqrt(9) = 57
(9 + 9! / sqrt(9)!!) / 9 = 57
9 × sqrt(9)! + 9 / sqrt(9) = 57
(9 + 9) × sqrt(9) + sqrt(9) = 57
9 × (9 - sqrt(9)) + sqrt(9) = 57

…and 37 more at this tier.

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

Make 56 with four 9s · Make 58 with four 9s

The Number Lab

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

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