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.

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.

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