Make 21 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 21. 21 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 21 — the solver checked every possible expression.

Solutions with concatenation and decimals

(9 + 9.9) / .9 = 21
(.9 + 9 + 9) / .9 = 21

Solutions with square roots, factorials, exponents

9 + 9 + 9 / sqrt(9) = 21
9 × sqrt(9) / .9 - 9 = 21
9 + 9 + 9 - sqrt(9)! = 21
9 / .9 × sqrt(9) - 9 = 21
9 + 9 - (sqrt(9)! - 9) = 21

…and 296 more at this tier.

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

How 21 compares

21 has 303 distinct solutions across all three tiers — #22 most plentiful of all 100 targets. Next door, 20 has 242 solutions and 22 has 11 solutions.

If 21 went down easily, make 22 with four 9s — 11 solutions, the nearest step up in scarcity.

Make 20 with four 9s · Make 22 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.