Make 81 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 81. 81 can be made with nothing but four 9s, + - × ÷, and parentheses.

Solutions using only + - × ÷

9 × 9 × 9 / 9 = 81
9 × 9 + 9 - 9 = 81
9 + 9 × 9 - 9 = 81
9 × (9 + 9 - 9) = 81
9 × 9 - (9 - 9) = 81

…and 5 more at this tier.

Solutions with concatenation and decimals

99 - 9 - 9 = 81
9 × 9 / .9 - 9 = 81
99 - (9 + 9) = 81
.9 × (99 - 9) = 81
.9 × 9 × 9 / .9 = 81

…and 27 more at this tier.

Solutions with square roots, factorials, exponents

9! × 9 × 9 / 9! = 81
9! + 9 × 9 - 9! = 81
9! - 9! + 9 × 9 = 81
9! / 9! × 9 × 9 = 81
9 × 9! × 9 / 9! = 81

…and 691 more at this tier.

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

How 81 compares

81 has 738 distinct solutions across all three tiers — #13 most plentiful of all 100 targets. 10 of them use nothing but + - × ÷. Next door, 80 has 711 solutions and 82 has 21 solutions.

If 81 went down easily, make 82 with four 9s — 21 solutions, the nearest step up in scarcity.

Make 80 with four 9s · Make 82 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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hand me something weird — a random pick from the directory. Could be the horse.

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