Make 16 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 16. 16 can be made with nothing but four 4s, + - × ÷, and parentheses.

Solutions using only + - × ÷

4 × 4 × 4 / 4 = 16
4 × 4 + 4 - 4 = 16
4 + 4 × 4 - 4 = 16
4 + 4 + 4 + 4 = 16
4 × (4 + 4 - 4) = 16

…and 6 more at this tier.

Solutions with concatenation and decimals

.4 × (44 - 4) = 16
.4 × 4 × 4 / .4 = 16
.4 × 4 / .4 × 4 = 16
.4 + 4 × 4 - .4 = 16
.4 - .4 + 4 × 4 = 16

…and 17 more at this tier.

Solutions with square roots, factorials, exponents

44 - 4! - 4 = 16
44 - 4 - 4! = 16
4 ^ 4 / 4 / 4 = 16
4! / .4 - 44 = 16
4! × 4 × 4 / 4! = 16

…and 2651 more at this tier.

2689 distinct solutions found in total, after removing trivial rearrangements.

How 16 compares

16 has 2,689 distinct solutions across all three tiers — #5 most plentiful of the 95 solvable targets. 11 of them use nothing but + - × ÷. Next door, 15 has 227 solutions and 17 has 49 solutions. The nearest impossible target is 73, 57 away — proven unreachable, not just unsolved.

If 16 went down easily, make 15 with four 4s — 227 solutions, the nearest step up in scarcity.

Make 15 with four 4s · Make 17 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.