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.

How 53 compares

53 has 21 distinct solutions across all three tiers — #36 scarcest of all 100 targets. Next door, 52 has 2 solutions and 54 has 629 solutions.

If 53 went down easily, make 52 with four 9s — 2 solutions, the nearest step up in scarcity.

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

The Number Lab

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

Four Nines — the daily puzzle
Four Nines solver — every target, solved
Four Fours — the 1881 original
Four Fours solver — including the impossible five
Make 24 solver — any four digits
Today's 24 — one new hand a day

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Four Nines — the daily puzzle: four 9s, one target, new at midnight
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