Make 46 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 46. 46 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 46 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 46 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 / .9 + sqrt(9)! × sqrt(9)! = 46
sqrt(9)! + sqrt(9)!! / (9 + 9) = 46
(.9 + sqrt(9)!) × sqrt(9)! / .9 = 46
(.9 + sqrt(9)!) / .9 × sqrt(9)! = 46
(.9 + sqrt(9)!) / (.9 / sqrt(9)!) = 46

…and 7 more at this tier.

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

Make 45 with four 9s · Make 47 with four 9s

The Number Lab

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

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