burger fun / Four Fours / Solver

Make 20 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 20. 20 can be made with nothing but four 4s, + - × ÷, and parentheses.

Solutions using only + - × ÷

• 4 × (4 + 4 / 4) = 20

Solutions with concatenation and decimals

• 4 / .4 + 4 / .4 = 20
• (.4 / .4 + 4) × 4 = 20
• 4 × 4 / (.4 + .4) = 20
• 4 / ((.4 + .4) / 4) = 20

Solutions with square roots, factorials, exponents

• 4! × 4 / 4 - 4 = 20
• 4! + 4 - 4 - 4 = 20
• 4! - 4 × 4 / 4 = 20
• 4! - 4 + 4 - 4 = 20
• 4 × 4! / 4 - 4 = 20

…and 1048 more at this tier.

1058 distinct solutions found in total, after removing trivial rearrangements.

Make 19 with four 4s · Make 21 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.