Make 24

How to play

You get four numbers. Your goal is to combine them into exactly 24, using each number once and any of the four operations. Tap a number to pick it up, tap an operation, then tap a second number — the two are replaced by the result. Keep combining until a single tile is left. If it shows 24, you've solved it and a new puzzle appears. Solve as many as you can before the timer runs out.

Use Undo to take back your last move, Reset to restore the original four numbers, or Skip puzzle if one has you stumped — skipping doesn't cost you anything but time. Every puzzle is checked to be solvable before it's shown.

A worked example

Say the numbers are 3, 3, 8, 8. One route to 24: 8 ÷ 3 = 8/3, then 3 − 8/3 = 1/3, then 8 ÷ 1/3 = 24. Fractions are allowed along the way, which is exactly what makes some puzzles sneaky. Another classic set is 1, 5, 5, 5: 5 − 1/5 = 24/5, then × 5 = 24.

Strategy

• Aim for factors of 24. If you can make 6 and 4, 8 and 3, or 12 and 2 from subsets, you're one step away.
• Don't fear fractions. Dividing to create thirds, halves or fifths unlocks many of the hardest puzzles.
• Try 24 ± something that cancels. Making 25 and 1, or 20 and 4, is often easier than hitting 24 head-on.
• If you're stuck, Reset and start from a different pair. The first combination you try shapes everything after it.

What's a good score?

The history of the 24 game

Making 24 from four cards has long been played with an ordinary deck in China, where players deal four cards face up and race to call out a way to reach 24. In 1988 Robert Sun turned the idea into a commercial card game for classrooms in the United States, and it has since become a fixture of school maths clubs and competitions.

The number 24 is well chosen. It has many divisors (1, 2, 3, 4, 6, 8, 12 and 24), so there are lots of routes to it, and the large majority of four-card hands can be solved.

Frequently asked questions

Is Make 24 free?

Yes, completely free with no sign-up. It runs in your browser and your best score is saved on your device.

Do I have to use all four numbers?

Yes. A valid solution uses each of the four numbers exactly once, combined with additions, subtractions, multiplications and divisions.

Are fractions allowed?

Yes. Intermediate results can be fractions — in fact several puzzles can only be solved by dividing to create a fraction along the way.

Is every puzzle solvable?

Yes. Each set of four numbers is verified to have at least one way to make 24 before it's shown to you.