burger fun / Four Nines / Solver

Make 3 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 3. 3 can be made with nothing but four 9s, + - × ÷, and parentheses.

Solutions using only + - × ÷

• (9 + 9 + 9) / 9 = 3

Solutions with concatenation and decimals

• (.9 + .9 + .9) / .9 = 3

Solutions with square roots, factorials, exponents

• (9! + 9! + 9!) / 9! = 3
• 9 × 9 / 9 / sqrt(9) = 3
• 9 × 9 / sqrt(9) / 9 = 3
• 9 × sqrt(9 / 9 / 9) = 3
• 9 + 9 / sqrt(9) - 9 = 3

…and 6300 more at this tier.

6307 distinct solutions found in total, after removing trivial rearrangements.

Make 2 with four 9s · Make 4 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.