Make 23 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 23. 23 cannot be made with + - × ÷, concatenation, or decimals (the solver checked every expression) — solutions need square roots, factorials, or exponents.

Solutions using only + - × ÷

No expression made of four plain 9s and + - × ÷ reaches 23 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 23 either — every combination was checked.

Solutions with square roots, factorials, exponents

(9 + 9) / .9 + sqrt(9) = 23
(sqrt(9)! ^ sqrt(9) - 9) / 9 = 23
(.9 + sqrt(9)!) × sqrt(9) / .9 = 23
(.9 + sqrt(9)!) / .9 × sqrt(9) = 23
(.9 + sqrt(9)!) / (.9 / sqrt(9)) = 23

…and 9 more at this tier.

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

Make 22 with four 9s · Make 24 with four 9s

The Number Lab

Same idea, different constraints: four 9s, four 4s, or any four digits you like.

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Today's 24 — one new hand a day

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