Make 56 with four 9s

The classic four nines puzzle: build an expression from exactly four 9s that equals 56. 56 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 56 — the solver checked every possible expression.

Solutions with concatenation and decimals

Concatenation and decimals do not help for 56 either — every combination was checked.

Solutions with square roots, factorials, exponents

9! / (9 - sqrt(9))! / 9 = 56
9! / 9 / (9 - sqrt(9))! = 56
(9 - 9 / 9)! / sqrt(9)!! = 56
9! / (9 / sqrt(9))!! / 9 = 56
9! / 9 / (9 / sqrt(9))!! = 56

…and 70 more at this tier.

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

How 56 compares

56 has 75 distinct solutions across all three tiers — #40 most plentiful of all 100 targets. Next door, 55 has 17 solutions and 57 has 42 solutions.

If 56 went down easily, make 55 with four 9s — 17 solutions, the nearest step up in scarcity.

Make 55 with four 9s · Make 57 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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