Make 52 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 52. 52 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 52 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 52 either — every combination was checked.

Solutions with square roots, factorials, exponents

(9 - sqrt(9) / 9) × sqrt(9)! = 52
9 × sqrt(9)! - sqrt(9)! / sqrt(9) = 52

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

Make 51 with four 9s · Make 53 with four 9s

The Number Lab

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