Make 72 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 72. 72 can be made with nothing but four 9s, + - × ÷, and parentheses.

Solutions using only + - × ÷

9 × (9 - 9 / 9) = 72

Solutions with concatenation and decimals

.9 × 9 × 9 - .9 = 72
9 × (9 - .9) - .9 = 72
9 × (9 - .9 / .9) = 72

Solutions with square roots, factorials, exponents

9 × (9 - 9! / 9!) = 72
9 × (9 - (9 - 9)!) = 72
99 - 9 × sqrt(9) = 72
9 × 9 - sqrt(9 × 9) = 72
9 × sqrt(9 × 9) - 9 = 72

…and 342 more at this tier.

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

How 72 compares

72 has 351 distinct solutions across all three tiers — #21 most plentiful of all 100 targets. Exactly one of them uses nothing but + - × ÷. Next door, 71 has 30 solutions and 73 has 5 solutions.

If 72 went down easily, make 71 with four 9s — 30 solutions, the nearest step up in scarcity.

Make 71 with four 9s · Make 73 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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