Make 4 with four 4s

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

Solutions using only + - × ÷

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

Solutions with concatenation and decimals

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

…and 7 more at this tier.

Solutions with square roots, factorials, exponents

4! + 4! - 44 = 4
4! - 4 × 4 - 4 = 4
4! - 4 - 4 × 4 = 4
(4 - 4) ^ 4 + 4 = 4
(4 / 4) ^ 4 × 4 = 4

…and 4978 more at this tier.

4999 distinct solutions found in total, after removing trivial rearrangements.

How 4 compares

4 has 4,999 distinct solutions across all three tiers — #4 most plentiful of the 95 solvable targets. 4 of them use nothing but + - × ÷. Next door, 3 has 1,012 solutions and 5 has 1,410 solutions. The nearest impossible target is 73, 69 away — proven unreachable, not just unsolved.

If 4 went down easily, make 3 with four 4s — 1,012 solutions, the nearest step up in scarcity.

Make 3 with four 4s · Make 5 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.