A game guide by Smart Hippo
How to play the 24 game: rules and worked examples
The aim of the 24 game is to combine four given numbers using addition, subtraction, multiplication and division to make exactly 24. Use every number exactly once.
Updated
Four rules to start with
- Use each original card once. Two equal numbers still count as two separate cards.
- Use +, −, × and ÷. Do not join two cards together to form a larger number.
- Choose any order for the numbers and operations; parentheses show the order in a written expression.
- Smart 24 allows fractions and negative intermediate results. Division by zero is not allowed, and the final result must equal 24 exactly.
Try the first two Smart 24 levels
Both sets below come from actual levels in the game. Each walkthrough shows one valid solution.
Level 1: 6, 6, 9, 4
(9 × 4) − (6 + 6) = 24
The 9 and 4 can make 36. To reach 24 from there, subtract 12. The two remaining sixes add up to exactly 12.
- 9 × 4 = 36
- 6 + 6 = 12
- 36 − 12 = 24
Level 2: 8, 4, 10, 4
(8 − 4) × (10 − 4) = 24
Start with 24 = 4 × 6. Make 4 with 8 − 4 and 6 with 10 − the other 4, then multiply. Each of the two fours is used once.
Fractions can open another route
The classic set 3, 3, 8, 8 illustrates a useful approach with fractions.
8 ÷ (3 − 8 ÷ 3) = 24
First, 8 ÷ 3 = 8/3. Then 3 − 8/3 = 1/3. Finally, 8 ÷ 1/3 = 24. Keep the fraction exact rather than rounding it to 2.67.
Try building 3 × 8, 4 × 6 or 2 × 12. You can also make a nearby number and add or subtract the difference. No single order solves every puzzle; undoing a move and trying another route is part of the game.
Common mistakes to check
- Reaching 24 with a card left over does not complete the puzzle.
- Subtraction and division depend on order: 8 − 3 differs from 3 − 8, just as 8 ÷ 3 differs from 3 ÷ 8.
- Four random numbers are not always solvable. Smart 24’s 1,040 campaign puzzles have all been verified to have a solution.