Make 67 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 67. 67 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 67 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 67 either — every combination was checked.

Solutions with square roots, factorials, exponents

sqrt(9 + 9! / 9 / 9) = 67
sqrt(9 + 9! / (9 × 9)) = 67
sqrt(9! + 9 ^ sqrt(9)) / 9 = 67
sqrt(9! + 9 + sqrt(9)!!) / 9 = 67
sqrt(9 + 9! + sqrt(9)!!) / 9 = 67

…and 3 more at this tier.

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

Make 66 with four 9s · Make 68 with four 9s

The Number Lab

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