Make 32 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 32. 32 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 32 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 32 either — every combination was checked.

Solutions with square roots, factorials, exponents

(99 - sqrt(9)) / sqrt(9) = 32
sqrt(9)! × (sqrt(9)! - sqrt(9)! / 9) = 32
sqrt((sqrt(9)! / sqrt(9)) ^ (9 / .9)) = 32

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

Make 31 with four 9s · Make 33 with four 9s

The Number Lab

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