burger fun / Four Fours / Solver
Make 68 with four 4s
The classic four fours puzzle: build an expression from exactly four 4s that equals 68. 68 can be made with nothing but four 4s, + - × ÷, and parentheses.
Solutions using only + - × ÷
4 + 4 × 4 × 4 = 68
Solutions with square roots, factorials, exponents
4 + 4 ^ 4 / 4 = 684! / .4 + 4 + 4 = 684 × 4! - 4! - 4 = 684 × 4! - 4 - 4! = 684 + 4 + 4! / .4 = 68
…and 41 more at this tier.
47 distinct solutions found in total, after removing trivial rearrangements.
How 68 compares
68 has 47 distinct solutions across all three tiers — #43 scarcest of the 95 solvable targets. Exactly one of them uses nothing but + - × ÷. Next door, 67 has just one solution and 69 has 5 solutions. The nearest impossible target is 73, 5 away — proven unreachable, not just unsolved.
If 68 went down easily, make 67 with four 4s — just one solution, the nearest step up in scarcity.
Make 67 with four 4s · Make 69 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.