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.

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.

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Today's 24 — one new hand a day

Play the daily Four Nines puzzle, pick another number in the solver, or find more free math games.