Make 53 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 53. 53 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 53 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 53 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 × sqrt(9)! - 9 / 9 = 53
9 × sqrt(9)! - .9 / .9 = 53
9 × sqrt(9)! - 9! / 9! = 53
9 × sqrt(9)! - (9 - 9)! = 53
9 × sqrt(9)! - (.9 - .9)! = 53

…and 16 more at this tier.

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

Make 52 with four 9s · Make 54 with four 9s

The Number Lab

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