burger fun / Four Nines / Solver

Make 72 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 72. 72 can be made with nothing but four 9s, + - × ÷, and parentheses.

Solutions using only + - × ÷

• 9 × (9 - 9 / 9) = 72

Solutions with concatenation and decimals

• .9 × 9 × 9 - .9 = 72
• 9 × (9 - .9) - .9 = 72
• 9 × (9 - .9 / .9) = 72

Solutions with square roots, factorials, exponents

• 9 × (9 - 9! / 9!) = 72
• 9 × (9 - (9 - 9)!) = 72
• 99 - 9 × sqrt(9) = 72
• 9 × 9 - sqrt(9 × 9) = 72
• 9 × sqrt(9 × 9) - 9 = 72

…and 342 more at this tier.

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

Make 71 with four 9s · Make 73 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.