burger fun / Four Fours / Solver

Make 80 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 80. 80 can be made with nothing but four 4s, + - × ÷, and parentheses.

Solutions using only + - × ÷

  • 4 × (4 + 4 × 4) = 80

Solutions with concatenation and decimals

  • (4 + 4) × 4 / .4 = 80
  • (4 + 4) / .4 × 4 = 80
  • 4 × (4 + 4) / .4 = 80
  • (4 + 4) / (.4 / 4) = 80
  • 4 / (.4 / (4 + 4)) = 80

Solutions with square roots, factorials, exponents

  • 4 × 4! - 4 × 4 = 80
  • 4 × (44 - 4!) = 80
  • 4! + 4! / .4 - 4 = 80
  • 4! - 4 + 4! / .4 = 80
  • (4! + 4 + 4) / .4 = 80

…and 80 more at this tier.

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

How 80 compares

80 has 91 distinct solutions across all three tiers — #39 most plentiful of the 95 solvable targets. Exactly one of them uses nothing but + - × ÷. Next door, 79 has 2 solutions and 81 has 39 solutions. The nearest impossible target is 77, 3 away — proven unreachable, not just unsolved.

If 80 went down easily, make 79 with four 4s — 2 solutions, the nearest step up in scarcity.

Make 79 with four 4s · Make 81 with four 4s

The Number Lab

Same idea, different constraints: four 9s, four 4s, or any four digits you like.

Got what you came for?

Stay for something you did not search for.

  • Four Nines — the daily sibling: four 9s, one target, new at midnight
  • The Reflex Lab — nine ways to measure your hands and memory, none of them polite about it
  • hand me something weird — a random pick from the directory. Could be the horse.

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