Make 69 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 69. 69 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 69 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 69 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 × 9 - 9 - sqrt(9) = 69
9 × 9 - sqrt(9) - 9 = 69
9 × 9 - (9 + sqrt(9)) = 69
9 + 9 × sqrt(9)! / .9 = 69
9 + 9 / .9 × sqrt(9)! = 69

…and 29 more at this tier.

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

Make 68 with four 9s · Make 70 with four 9s

The Number Lab

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

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