Make 5 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 5. 5 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 5 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 5 either — every combination was checked.

Solutions with square roots, factorials, exponents

9 - 9 / 9 - sqrt(9) = 5
9 - sqrt(9) - 9 / 9 = 5
99 / 9 - sqrt(9)! = 5
(9 + 9) / 9 + sqrt(9) = 5
(9 / .9)! / (9! + 9!) = 5

…and 616 more at this tier.

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

How 5 compares

5 has 621 distinct solutions across all three tiers — #18 most plentiful of all 100 targets. Next door, 4 has 722 solutions and 6 has 9,378 solutions.

If 5 went down easily, make 11 with four 9s — 215 solutions, the nearest step up in scarcity.

Make 4 with four 9s · Make 6 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
The Reflex Lab — nine ways to measure your hands and memory, none of them polite about it
hand me something weird — a random pick from the directory. Could be the horse.

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