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.

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.

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