Make 75 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 75. 75 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 75 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 75 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 × 9 + sqrt(9) - 9 = 75
9 × 9 - 9 + sqrt(9) = 75
9 × 9 - (9 - sqrt(9)) = 75
sqrt(9) - (9 - 9 × 9) = 75
9 × (9 - sqrt(9)! / 9) = 75

…and 48 more at this tier.

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

Make 74 with four 9s · Make 76 with four 9s

The Number Lab

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