24 Game

You get four numbers. Combine all four, each exactly once, with addition, subtraction, multiplication, division and parentheses to make 24. With 3, 3, 8, 8 the answer is 8 ÷ (3 − 8 ÷ 3) = 24, one of the hardest classic hands.

How to play the 24 game

1. Use each of the four numbers exactly once.
2. Combine them with +, −, ×, ÷ and parentheses. Tap the cards and signs, or type.
3. Press Check. If the value is exactly 24, you solved it. Stuck? Press Show a solution or New numbers.

Strategies that find 24 fast

• Look for factor pairs: 24 = 1 × 24 = 2 × 12 = 3 × 8 = 4 × 6. Try to make one factor from two cards and the other from the rest. With 2, 5, 6, 8: (8 − 5) × (6 + 2) = 24.
• Sums and differences: 24 = 20 + 4 = 30 − 6 = 12 + 12.
• Fractions help on hard hands: 8 ÷ (3 − 8/3) = 8 ÷ (1/3) = 24.
• Use 1s as multipliers that change nothing, or to adjust by one.

How the solver works

The solver tries every way to pick two numbers, combine them with each operation, and repeat with the result until one number is left. It uses exact fractions, so 8 ÷ 3 stays 8/3 instead of a rounded decimal. With four numbers that is only a few thousand combinations, which a computer checks instantly.

24 game practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

Can every set of four numbers make 24?

No. For example 1, 1, 1, 1 and 1, 1, 1, 2 cannot. The game only deals hands that have a solution.

Are fractions allowed?

Yes, in the middle of a calculation. 8 ÷ (3 − 8 ÷ 3) uses 8/3 along the way and still ends at exactly 24.

Can I combine cards into a two-digit number?

No. In the standard rules, 1 and 2 cannot become 12.

What does the solver do?

It finds every way to reach a target from 2 to 6 numbers using + − × ÷, with exact fraction arithmetic.

Is the 24 game good for kids?

Yes. It builds number sense, multiplication facts and the order of operations, and the easy level avoids division.

Sources

• Wikipedia: 24 (puzzle)

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