Make 81 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 81. 81 cannot be made with + - × ÷, concatenation, or decimals (the solver checked every expression) — solutions need square roots, factorials, or exponents.

Solutions using only + - × ÷

No expression made of four plain 4s and + - × ÷ reaches 81 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 81 either — every combination was checked.

Solutions with square roots, factorials, exponents

(4 - 4 / 4) ^ 4 = 81
(4 / 4 - 4) ^ 4 = 81
(.4 / .4 - 4) ^ 4 = 81
(4! / 4! - 4) ^ 4 = 81
(4 - .4 / .4) ^ 4 = 81

…and 34 more at this tier.

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

How 81 compares

81 has 39 distinct solutions across all three tiers — #38 scarcest of the 95 solvable targets. Next door, 80 has 91 solutions and 82 has 6 solutions. The nearest impossible target is 77, 4 away — proven unreachable, not just unsolved.

If 81 went down easily, make 82 with four 4s — 6 solutions, the nearest step up in scarcity.

Make 80 with four 4s · Make 82 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

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.