Make 60 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 60. 60 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 60 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 60 either — every combination was checked.

Solutions with square roots, factorials, exponents

(9 + 9) × sqrt(9) / .9 = 60
(9 + 9) / .9 × sqrt(9) = 60
(9 + 9 / 9) × sqrt(9)! = 60
(9 - sqrt(9)) × 9 / .9 = 60
(9 - sqrt(9)) / .9 × 9 = 60

…and 225 more at this tier.

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

Make 59 with four 9s · Make 61 with four 9s

The Number Lab

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

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