burger fun / 24 Game Solver / Notable hands
Make 24 with 1, 1, 1, 1
The 24 Game hand 1, 1, 1, 1: use each digit exactly once with + - × ÷ and parentheses to reach exactly 24. This hand cannot make 24 — the solver checked every possible expression with + - × ÷ and parentheses using exact fraction arithmetic, so that is a proof, not a shrug.
Why 1, 1, 1, 1 is impossible
No combination of 1, 1, 1, 1 with + - × ÷ and parentheses equals 24. Four numbers and four operations make a small, finite space of expressions; the solver evaluated all of them with exact fractions and none reached 24. That is a checked mathematical fact — this hand is famous precisely for being a lost cause.
Browse the hardest 24 game puzzles, drill hands like this in practice mode, or solve any hand with the 24 game solver.
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