Make 51 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 51. 51 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 51 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 51 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 × sqrt(9)! / .9 - 9 = 51
9 / .9 × sqrt(9)! - 9 = 51
9 × (9 - sqrt(9) / .9) = 51
9 / (.9 / sqrt(9)!) - 9 = 51
sqrt(9)! / (.9 / 9) - 9 = 51

…and 40 more at this tier.

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

Make 50 with four 9s · Make 52 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

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