Make 3 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 3. 3 can be made with nothing but four 9s, + - × ÷, and parentheses.

Solutions using only + - × ÷

(9 + 9 + 9) / 9 = 3

Solutions with concatenation and decimals

(.9 + .9 + .9) / .9 = 3

Solutions with square roots, factorials, exponents

(9! + 9! + 9!) / 9! = 3
9 × 9 / 9 / sqrt(9) = 3
9 × 9 / sqrt(9) / 9 = 3
9 × sqrt(9 / 9 / 9) = 3
9 + 9 / sqrt(9) - 9 = 3

…and 6300 more at this tier.

6307 distinct solutions found in total, after removing trivial rearrangements.

How 3 compares

3 has 6,307 distinct solutions across all three tiers — #3 most plentiful of all 100 targets. Exactly one of them uses nothing but + - × ÷. Next door, 2 has 2,101 solutions and 4 has 722 solutions.

If 3 went down easily, make 2 with four 9s — 2,101 solutions, the nearest step up in scarcity.

Make 2 with four 9s · Make 4 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.