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.

How 75 compares

75 has 53 distinct solutions across all three tiers — #46 most plentiful of all 100 targets. Next door, 74 has 33 solutions and 76 has 3 solutions.

If 75 went down easily, make 76 with four 9s — 3 solutions, the nearest step up in scarcity.

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

The Number Lab

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

Four Nines — the daily puzzle
Four Nines solver — every target, solved
Four Fours — the 1881 original
Four Fours solver — including the impossible five
Make 24 solver — any four digits
Today's 24 — one new hand a day

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