Make 9 with four 9s

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

Solutions using only + - × ÷

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

Solutions with concatenation and decimals

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

…and 17 more at this tier.

Solutions with square roots, factorials, exponents

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

…and 3230 more at this tier.

3261 distinct solutions found in total, after removing trivial rearrangements.

How 9 compares

9 has 3,261 distinct solutions across all three tiers — #5 most plentiful of all 100 targets. 4 of them use nothing but + - × ÷. Next door, 8 has 716 solutions and 10 has 803 solutions.

If 9 went down easily, make 8 with four 9s — 716 solutions, the nearest step up in scarcity.

Make 8 with four 9s · Make 10 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

Got what you came for?

Stay for something you did not search for.

Four Nines — the daily puzzle: four 9s, one target, new at midnight
The Reflex Lab — nine ways to measure your hands and memory, none of them polite about it
hand me something weird — a random pick from the directory. Could be the horse.

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