Make 90 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 90. 90 can be made with nothing but four 9s, + - × ÷, and parentheses.

Solutions using only + - × ÷

9 × (9 + 9 / 9) = 90

Solutions with concatenation and decimals

.9 + .9 × 99 = 90
.9 + 9 × 9.9 = 90
9 / (9 / 9 - .9) = 90
(.9 + 9) × 9 + .9 = 90
(.9 / .9 + 9) × 9 = 90

…and 1 more at this tier.

Solutions with square roots, factorials, exponents

9 × (9 + 9! / 9!) = 90
((9 - 9)! + 9) × 9 = 90
(9 / .9)! × 9 / 9! = 90
(9 / .9)! / 9! × 9 = 90
9 / (9! / 9! - .9) = 90

…and 173 more at this tier.

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

How 90 compares

90 has 185 distinct solutions across all three tiers — #28 most plentiful of all 100 targets. Exactly one of them uses nothing but + - × ÷. Next door, 89 has 29 solutions and 91 has 3 solutions.

If 90 went down easily, make 89 with four 9s — 29 solutions, the nearest step up in scarcity.

Make 89 with four 9s · Make 91 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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