burger fun / Four Fours / Solver

Make 3 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 3. 3 can be made with nothing but four 4s, + - × ÷, and parentheses.

Solutions using only + - × ÷

• (4 × 4 - 4) / 4 = 3
• (4 + 4 + 4) / 4 = 3

Solutions with concatenation and decimals

• (.4 × 4 - .4) / .4 = 3
• (.4 + .4 + .4) / .4 = 3

Solutions with square roots, factorials, exponents

• 4 - (4 / 4) ^ 4 = 3
• 4 - 4 ^ (4 - 4) = 3
• (4 + 4!) / 4 - 4 = 3
• 4 - (4 - 4)! ^ 4 = 3
• 4 - .4 ^ (4 - 4) = 3

…and 1003 more at this tier.

1012 distinct solutions found in total, after removing trivial rearrangements.

Make 2 with four 4s · Make 4 with four 4s

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

Read up on the 1881 original, pick another number in the solver, or find more free math games.