Make 54 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 54. 54 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 54 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 54 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 × 9 - 9 × sqrt(9) = 54
9 × 9 × sqrt(9)! / 9 = 54
9 × 9 / 9 × sqrt(9)! = 54
9 × sqrt(9)! × 9 / 9 = 54
9 × sqrt(9)! + 9 - 9 = 54

…and 624 more at this tier.

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

How 54 compares

54 has 629 distinct solutions across all three tiers — #17 most plentiful of all 100 targets. Next door, 53 has 21 solutions and 55 has 17 solutions.

If 54 went down easily, make 53 with four 9s — 21 solutions, the nearest step up in scarcity.

Make 53 with four 9s · Make 55 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
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Four Fours solver — including the impossible five
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