Make 21 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 21. 21 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 21 — the solver checked every possible expression.

Solutions with concatenation and decimals

4 / .4 / .4 - 4 = 21
(4 + 4.4) / .4 = 21
(.4 + 4 + 4) / .4 = 21
4 / (.4 × .4) - 4 = 21

Solutions with square roots, factorials, exponents

4! + 4 / 4 - 4 = 21
4! - 4 + 4 / 4 = 21
.4 / .4 + 4! - 4 = 21
.4 / .4 - 4 + 4! = 21
4! + 4! / 4! - 4 = 21

…and 73 more at this tier.

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

Make 20 with four 4s · Make 22 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.