burger fun / Four Fours / Solver
Make 84 with four 4s
The classic four fours puzzle: build an expression from exactly four 4s 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 4s 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
4 + 4 × (4! - 4) = 844 - 4 × (4 - 4!) = 8444 × sqrt(4) - 4 = 84(.4 × 4! + 4!) / .4 = 844 × 4! - 4! / sqrt(4) = 84
…and 31 more at this tier.
36 distinct solutions found in total, after removing trivial rearrangements.
How 84 compares
84 has 36 distinct solutions across all three tiers — #36 scarcest of the 95 solvable targets. Next door, 83 has 2 solutions and 85 has 2 solutions. The nearest impossible target is 87, 3 away — proven unreachable, not just unsolved.
If 84 went down easily, make 83 with four 4s — 2 solutions, the nearest step up in scarcity.
Make 83 with four 4s · Make 85 with four 4s
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 sibling: 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.
Read up on the 1881 original, pick another number in the solver, or find more free math games.