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.

How 3 compares

3 has 1,012 distinct solutions across all three tiers — #12 most plentiful of the 95 solvable targets. 2 of them use nothing but + - × ÷. Next door, 2 has 6,903 solutions and 4 has 4,999 solutions. The nearest impossible target is 73, 70 away — proven unreachable, not just unsolved.

If 3 went down easily, make 7 with four 4s — 176 solutions, the nearest step up in scarcity.

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

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.