Make 83 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 83. 83 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 83 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 83 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 × 9 + sqrt(9)! / sqrt(9) = 83
9 / sqrt(9) + sqrt(9)!! / 9 = 83
(9 - sqrt(9))! / 9 + sqrt(9) = 83
9 + sqrt(9)!! / 9 - sqrt(9)! = 83
9 - sqrt(9)! + sqrt(9)!! / 9 = 83

…and 34 more at this tier.

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

Make 82 with four 9s · Make 84 with four 9s

The Number Lab

Same idea, different constraints: four 9s, four 4s, or any four digits you like.

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