Make 7 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 7. 7 can be made with nothing but four 9s, + - × ÷, and parentheses.

Solutions using only + - × ÷

9 - (9 + 9) / 9 = 7

Solutions with concatenation and decimals

9 - (.9 + .9) / .9 = 7

Solutions with square roots, factorials, exponents

9 - (9! + 9!) / 9! = 7
9 + 9 / 9 - sqrt(9) = 7
9 - sqrt(9) + 9 / 9 = 7
9 / .9 - 9 / sqrt(9) = 7
.9 / .9 + 9 - sqrt(9) = 7

…and 565 more at this tier.

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

How 7 compares

7 has 572 distinct solutions across all three tiers — #19 most plentiful of all 100 targets. Exactly one of them uses nothing but + - × ÷. Next door, 6 has 9,378 solutions and 8 has 716 solutions.

If 7 went down easily, make 11 with four 9s — 215 solutions, the nearest step up in scarcity.

Make 6 with four 9s · Make 8 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.