Make 82 with four 4s

The classic four fours puzzle: build an expression from exactly four 4s that equals 82. 82 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 82 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 82 either — every combination was checked.

Solutions with square roots, factorials, exponents

4! + 4! / .4 - sqrt(4) = 82
4! - sqrt(4) + 4! / .4 = 82
4 × (4! - 4) + sqrt(4) = 82
sqrt(4) - 4 × (4 - 4!) = 82
4! - (sqrt(4) - 4! / .4) = 82

…and 1 more at this tier.

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

Make 81 with four 4s · Make 83 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.