Make 82 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 82. 82 can be made with nothing but four 9s, + - × ÷, and parentheses.

Solutions using only + - × ÷

9 × 9 + 9 / 9 = 82

Solutions with concatenation and decimals

.9 / .9 + 9 × 9 = 82

Solutions with square roots, factorials, exponents

9! / 9! + 9 × 9 = 82
(9 - 9)! + 9 × 9 = 82
(.9 - .9)! + 9 × 9 = 82
(9! - 9!)! + 9 × 9 = 82
(9 + 9 ^ sqrt(9)) / 9 = 82

…and 14 more at this tier.

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

How 82 compares

82 has 21 distinct solutions across all three tiers — #36 scarcest of all 100 targets. Exactly one of them uses nothing but + - × ÷. Next door, 81 has 738 solutions and 83 has 39 solutions.

If 82 went down easily, make 85 with four 9s — 4 solutions, the nearest step up in scarcity.

Make 81 with four 9s · Make 83 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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