Make 8 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 8. 8 can be made with nothing but four 4s, + - × ÷, and parentheses.

Solutions using only + - × ÷

4 × 4 - 4 - 4 = 8
4 + 4 × 4 / 4 = 8
4 + 4 + 4 - 4 = 8
(4 + 4) × 4 / 4 = 8
(4 + 4) / 4 × 4 = 8

…and 8 more at this tier.

Solutions with concatenation and decimals

4 + 4.4 - .4 = 8
4 - .4 + 4.4 = 8
.4 × 4 / .4 + 4 = 8
.4 + 4 + 4 - .4 = 8
.4 + 4 - .4 + 4 = 8

…and 28 more at this tier.

Solutions with square roots, factorials, exponents

4! + 4 + 4 - 4! = 8
4! - 4! + 4 + 4 = 8
4 + 4! × 4 / 4! = 8
4 + 4! + 4 - 4! = 8
4 + 4 × 4! / 4! = 8

…and 1924 more at this tier.

1975 distinct solutions found in total, after removing trivial rearrangements.

How 8 compares

8 has 1,975 distinct solutions across all three tiers — #7 most plentiful of the 95 solvable targets. 13 of them use nothing but + - × ÷. Next door, 7 has 176 solutions and 9 has 183 solutions. The nearest impossible target is 73, 65 away — proven unreachable, not just unsolved.

If 8 went down easily, make 7 with four 4s — 176 solutions, the nearest step up in scarcity.

Make 7 with four 4s · Make 9 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.