Make 62 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 62. 62 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 62 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 62 either — every combination was checked.

Solutions with square roots, factorials, exponents

sqrt(9)!! / 9 - 9 - 9 = 62
sqrt(9)!! / 9 - (9 + 9) = 62
9! / 9 / sqrt(9)!! + sqrt(9)! = 62
9! / sqrt(9)!! / 9 + sqrt(9)! = 62
9! / (9 × sqrt(9)!!) + sqrt(9)! = 62

…and 1 more at this tier.

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

Make 61 with four 9s · Make 63 with four 9s

The Number Lab

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

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