Make 40 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 40. 40 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 40 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 40 either — every combination was checked.

Solutions with square roots, factorials, exponents

4 × 4 × 4 - 4! = 40
4 ^ 4 / 4 - 4! = 40
4! + 4! - 4 - 4 = 40
4! - 4 + 4! - 4 = 40
4! / .4 + 4 - 4! = 40

…and 393 more at this tier.

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

How 40 compares

40 has 398 distinct solutions across all three tiers — #23 most plentiful of the 95 solvable targets. Next door, 39 has 11 solutions and 41 has 7 solutions. The nearest impossible target is 73, 33 away — proven unreachable, not just unsolved.

If 40 went down easily, make 39 with four 4s — 11 solutions, the nearest step up in scarcity.

Make 39 with four 4s · Make 41 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.