Make 20 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 20. 20 can be made with nothing but four 4s, + - × ÷, and parentheses.

Solutions using only + - × ÷

4 × (4 + 4 / 4) = 20

Solutions with concatenation and decimals

4 / .4 + 4 / .4 = 20
(.4 / .4 + 4) × 4 = 20
4 × 4 / (.4 + .4) = 20
4 / ((.4 + .4) / 4) = 20

Solutions with square roots, factorials, exponents

4! × 4 / 4 - 4 = 20
4! + 4 - 4 - 4 = 20
4! - 4 × 4 / 4 = 20
4! - 4 + 4 - 4 = 20
4 × 4! / 4 - 4 = 20

…and 1048 more at this tier.

1058 distinct solutions found in total, after removing trivial rearrangements.

How 20 compares

20 has 1,058 distinct solutions across all three tiers — #11 most plentiful of the 95 solvable targets. Exactly one of them uses nothing but + - × ÷. Next door, 19 has 83 solutions and 21 has 82 solutions. The nearest impossible target is 73, 53 away — proven unreachable, not just unsolved.

If 20 went down easily, make 19 with four 4s — 83 solutions, the nearest step up in scarcity.

Make 19 with four 4s · Make 21 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.