Make 34 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 34. 34 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 34 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 34 either — every combination was checked.

Solutions with square roots, factorials, exponents

(99 + sqrt(9)) / sqrt(9) = 34
(9 - sqrt(9) / .9) × sqrt(9)! = 34
sqrt(9)!! / (9 + 9) - sqrt(9)! = 34
(sqrt(9)! - .9) × sqrt(9)! / .9 = 34
(sqrt(9)! - .9) / .9 × sqrt(9)! = 34

…and 11 more at this tier.

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

How 34 compares

34 has 16 distinct solutions across all three tiers — #33 scarcest of all 100 targets. Next door, 33 has 253 solutions and 35 has 16 solutions.

If 34 went down easily, make 32 with four 9s — 3 solutions, the nearest step up in scarcity.

Make 33 with four 9s · Make 35 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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Four Nines — the daily puzzle: four 9s, one target, new at midnight
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hand me something weird — a random pick from the directory. Could be the horse.

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