burger fun / Four Nines / Solver
Make 84 with four 9s
The classic four nines puzzle: build an expression from exactly four 9s that equals 84. 84 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 84 — the solver checked every possible expression.
Solutions with concatenation and decimals
Concatenation and decimals do not help for 84 either — every combination was checked.
Solutions with square roots, factorials, exponents
9 × 9 + 9 / sqrt(9) = 8499 - 9 - sqrt(9)! = 8499 - sqrt(9)! - 9 = 849 × 9 + 9 - sqrt(9)! = 849 + 9 × 9 - sqrt(9)! = 84
…and 111 more at this tier.
116 distinct solutions found in total, after removing trivial rearrangements.
How 84 compares
84 has 116 distinct solutions across all three tiers — #30 most plentiful of all 100 targets. Next door, 83 has 39 solutions and 85 has 4 solutions.
If 84 went down easily, make 83 with four 9s — 39 solutions, the nearest step up in scarcity.
Make 83 with four 9s · Make 85 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
Got what you came for?
Stay for something you did not search for.
- 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.
Play the daily Four Nines puzzle, pick another number in the solver, or find more free math games.