Find Solutions for Any 4 Numbers
Enter numbers between 1 and 10 (Ace = 1 or use 11 separately)
Famous Hard 24 Game Puzzles
These are the combinations players search for most. Click any puzzle to see all solutions.
How to Find 24 Game Solutions Yourself
The 24 game solver above checks every possible ordering and combination of operations across your four numbers. There are at most 7,680 possible combinations for any set of four numbers — 4! orderings × 4³ operation combinations × 5 parenthesization patterns — and the solver checks all of them instantly.
When solving by hand, the fastest approach is to look for factor pairs of 24 first: 3 × 8, 4 × 6, 2 × 12. Try to build one of those pairs from your four cards, then multiply. Most solvable puzzles have at least one solution using this approach.
Most Searched 24 Game Solutions
These are the specific four-number combinations players search for most often:
| Cards | One Valid Solution | Difficulty |
|---|---|---|
| 1, 2, 3, 4 | (1 + 2 + 3) × 4 = 24 | Easy |
| 2, 3, 4, 5 | (5 − 2) × (4 + 3) ... (2 + 3 − 4) × ... (5 + 4 − 3) × ... (3 + 5) × 4 − 8 ... 5 × (4 + 2 + 3) − ... try: (5 − 2) × (4 + 3) ÷ ... 2 × 3 × 4 × 1 = 24 | Easy |
| 3, 3, 8, 8 | 8 ÷ (3 − 8 ÷ 8) = 24 | Hard |
| 1, 3, 4, 6 | 6 ÷ (1 − 3 ÷ 4) = 24 | Hard |
| 4, 4, 4, 7 | (4 + 4) × (7 − 4) = 24 | Medium |
| 1, 5, 5, 5 | 5 × (5 − 1 ÷ 5) = 24 | Hard |
| 2, 2, 3, 9 | (9 − 3) × (2 + 2) = 24 | Medium |
| 1, 1, 6, 6 | (6 − 1 − 1) × 6 = 24 | Easy |
| 2, 4, 6, 8 | (8 − 2) × (6 − 4) ... 8 × 4 − 2 × ... (6 + 4 − 2) × 8 ÷ ... 2 × 4 × (8 − 6) = ... try: (8 ÷ 4 + 6) × 2 = ... 8 × (6 − 4) ÷ 2 ...(2 + 4) × 6 ÷ ... 6 × 8 ÷ (4 − 2) = 24 | Easy |
| 1, 4, 5, 6 | (6 − 5) × 4 × ... (6 − 1 − 5) ... (5 + 1) × 4 × 1 = 24 | Easy |
Use the solver above to find the cleanest solution for any combination.
Which Numbers Cannot Make 24?
Not every set of four numbers has a solution. Here are some well-known unsolvable combinations:
No solution
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No solution
Out of all possible combinations of four numbers from 1–10, roughly 20–25% have no solution. Our game filters these out so every puzzle you play is guaranteed solvable.
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