Make 73 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 73. 73 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 73 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 73 either — every combination was checked.

Solutions with square roots, factorials, exponents

(.9 × sqrt(9)!! + 9) / 9 = 73
(sqrt(9)!! - 9) / 9 - sqrt(9)! = 73
(sqrt(9)! / sqrt(9)) ^ sqrt(9)! + 9 = 73
(sqrt(9) + sqrt(9)! ^ sqrt(9)) / sqrt(9) = 73
(sqrt(9) + sqrt(sqrt(9)! ^ sqrt(9)!)) / sqrt(9) = 73

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

How 73 compares

73 has 5 distinct solutions across all three tiers — #17 scarcest of all 100 targets. Next door, 72 has 351 solutions and 74 has 33 solutions.

If 73 went down easily, make 61 with four 9s — 2 solutions, the nearest step up in scarcity.

Make 72 with four 9s · Make 74 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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