Make 16 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 16. 16 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 9s and + - × ÷ reaches 16 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 16 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 + 9 / .9 - sqrt(9) = 16
9 + 9 / 9 + sqrt(9)! = 16
9 + sqrt(9)! + 9 / 9 = 16
9 - sqrt(9) + 9 / .9 = 16
.9 / .9 + 9 + sqrt(9)! = 16

…and 51 more at this tier.

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

How 16 compares

16 has 56 distinct solutions across all three tiers — #44 most plentiful of all 100 targets. Next door, 15 has 757 solutions and 17 has 67 solutions.

If 16 went down easily, make 22 with four 9s — 11 solutions, the nearest step up in scarcity.

Make 15 with four 9s · Make 17 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

Got what you came for?

Stay for something you did not search for.

Four Nines — the daily puzzle: 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.

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