Make 78 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 78. 78 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 78 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 78 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 × 9 - 9 / sqrt(9) = 78
9 × 9 + sqrt(9)! - 9 = 78
9 × 9 - 9 + sqrt(9)! = 78
9 × (9 - sqrt(9) / 9) = 78
9 × 9 - (9 - sqrt(9)!) = 78

…and 50 more at this tier.

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

Make 77 with four 9s · Make 79 with four 9s

The Number Lab

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