Make 45 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 45. 45 cannot be made with + - × ÷ alone (the solver checked every expression) — you will need to stick 9s together (like 99) or use decimals (like .9).

Solutions using only + - × ÷

No expression made of four plain 9s and + - × ÷ reaches 45 — the solver checked every possible expression.

Solutions with concatenation and decimals

9 × 9 / (.9 + .9) = 45
9 / ((.9 + .9) / 9) = 45

Solutions with square roots, factorials, exponents

9 × sqrt(9) + 9 + 9 = 45
9 + 9 + 9 × sqrt(9) = 45
99 - 9 × sqrt(9)! = 45
(9 + 9) × sqrt(9) - 9 = 45
9 × (9 - sqrt(9)) - 9 = 45

…and 101 more at this tier.

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

How 45 compares

45 has 108 distinct solutions across all three tiers — #31 most plentiful of all 100 targets. Next door, 44 has 2 solutions and 46 has 12 solutions.

If 45 went down easily, make 44 with four 9s — 2 solutions, the nearest step up in scarcity.

Make 44 with four 9s · Make 46 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.