burger fun / Four Fours / Solver
Make 53 with four 4s
The classic four fours puzzle: build an expression from exactly four 4s that equals 53. 53 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 53 — the solver checked every possible expression.
Solutions with concatenation and decimals
Concatenation and decimals do not help for 53 either — every combination was checked.
Solutions with square roots, factorials, exponents
4! + 4! + sqrt(4) / .4 = 534! × sqrt(4) + sqrt(4) / .4 = 53(4! - sqrt(4)) / .4 - sqrt(4) = 53
3 distinct solutions found in total, after removing trivial rearrangements.
How 53 compares
53 has 3 distinct solutions across all three tiers — #9 scarcest of the 95 solvable targets. Next door, 52 has 126 solutions and 54 has 29 solutions. The nearest impossible target is 73, 20 away — proven unreachable, not just unsolved.
If 53 went down easily, make 67 with four 4s — just one solution, the nearest step up in scarcity.
Make 52 with four 4s · Make 54 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.