Make 20 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 20. 20 cannot be made with + - × ÷ alone (the solver checked every expression) — you will need to stick 9s together (like 99) or use decimals (like .9).

Solutions using only + - × ÷

No expression made of four plain 9s and + - × ÷ reaches 20 — the solver checked every possible expression.

Solutions with concatenation and decimals

9 + 99 / 9 = 20
9 + 9.9 / .9 = 20
9 / .9 + 9 / .9 = 20
(.9 + 9) / .9 + 9 = 20

Solutions with square roots, factorials, exponents

(9 × sqrt(9) - 9) / .9 = 20
(9 + sqrt(9 × 9)) / .9 = 20
(9 + 9) / sqrt(.9 × .9) = 20
9 + 9 + sqrt(9)! / sqrt(9) = 20
(9 / (.9 + .9))! / sqrt(9)! = 20

…and 233 more at this tier.

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

Make 19 with four 9s · Make 21 with four 9s

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

Play the daily Four Nines puzzle, pick another number in the solver, or find more free math games.