Make 64 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 64. 64 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 64 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 64 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 × sqrt(9)! + 9 / .9 = 64
((9 + 9) / 9) ^ sqrt(9)! = 64
((.9 + .9) / .9) ^ sqrt(9)! = 64
((9! + 9!) / 9!) ^ sqrt(9)! = 64
(9 / 9 + sqrt(9)) ^ sqrt(9) = 64

…and 124 more at this tier.

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

Make 63 with four 9s · Make 65 with four 9s

The Number Lab

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

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