Make 86 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 86. 86 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 86 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 86 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 + sqrt(9)!! / 9 - sqrt(9) = 86
9 - sqrt(9) + sqrt(9)!! / 9 = 86
(9 - sqrt(9))! / 9 + sqrt(9)! = 86
9 - (sqrt(9) - sqrt(9)!! / 9) = 86
sqrt(9)!! / 9 - (sqrt(9) - 9) = 86

…and 26 more at this tier.

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

Make 85 with four 9s · Make 87 with four 9s

The Number Lab

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