Make 45 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 45. 45 cannot be made with + - × ÷ alone (the solver checked every expression) — you will need to stick 4s together (like 44) or use decimals (like .4).

Solutions using only + - × ÷

No expression made of four plain 4s and + - × ÷ reaches 45 — the solver checked every possible expression.

Solutions with concatenation and decimals

4 / 4 + 44 = 45
.4 / .4 + 44 = 45

Solutions with square roots, factorials, exponents

4! / 4! + 44 = 45
(4 - 4)! + 44 = 45
(.4 - .4)! + 44 = 45
(4! - 4!)! + 44 = 45
(4! / 4)! / 4 / 4 = 45

…and 19 more at this tier.

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

Make 44 with four 4s · Make 46 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

Read up on the 1881 original, pick another number in the solver, or find more free math games.