Make 23 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 23. 23 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 23 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 23 either — every combination was checked.

Solutions with square roots, factorials, exponents

(4 × 4! - 4) / 4 = 23
4! - (4 / 4) ^ 4 = 23
4! - 4 ^ (4 - 4) = 23
4! - (4 - 4)! ^ 4 = 23
4! - .4 ^ (4 - 4) = 23

…and 348 more at this tier.

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

How 23 compares

23 has 353 distinct solutions across all three tiers — #25 most plentiful of the 95 solvable targets. Next door, 22 has 899 solutions and 24 has 7,847 solutions. The nearest impossible target is 73, 50 away — proven unreachable, not just unsolved.

If 23 went down easily, make 21 with four 4s — 82 solutions, the nearest step up in scarcity.

Make 22 with four 4s · Make 24 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.