Make 68 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 68. 68 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 68 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 68 either — every combination was checked.

Solutions with square roots, factorials, exponents

sqrt(9)!! / 9 - 9 - sqrt(9) = 68
sqrt(9)!! / 9 - sqrt(9) - 9 = 68
sqrt(9)!! / 9 - (9 + sqrt(9)) = 68
sqrt(9)!! / 9 - sqrt(9)! - sqrt(9)! = 68
sqrt(9)!! / 9 - (sqrt(9)! + sqrt(9)!) = 68

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

Make 67 with four 9s · Make 69 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.