How to Play the 24 Game: Rules, a Worked Example, and First Strategies

What is the 24 game?

The 24 game is a mental-math card game: given four numbers, combine them with arithmetic to make exactly 24. It originated in China (算24点) and became a classroom staple worldwide because a single deal is a complete, self-contained puzzle that takes seconds to minutes.

The rules in four steps

1. Deal four numbers — any four numbers from 1 to 13 (face cards count as J = 11, Q = 12, K = 13).
2. Combine with operations — use +, −, ×, ÷ in any order, with parentheses to group. Each number must be used exactly once.
3. Make exactly 24 — the final result must equal 24. Intermediate results may be fractions; the classic classroom variant requires whole-number intermediates only.
4. Check your answer — paste the numbers into the solver to see every solution.

A worked example: 3 3 8 8

The most famous 24 game hand looks impossible at first — until you allow a fraction in the middle:

1. Divide 8 by 3 → 8/3
2. Subtract: 3 − 8/3 = 1/3
3. Divide 8 by that → 8 ÷ (1/3) = 24

In one expression: 8 ÷ (3 − 8 ÷ 3) = 24. Every whole-number path on this hand fails — the fraction is not a trick, it is the only way. This is why the fraction rule matters, and why 3 3 8 8 is classified as an expert hand in our difficulty system. See the full 3 3 8 8 solution page for the complete breakdown.

First strategies that actually work

• Aim for a factor pair of 24. The fastest route is usually to build two blocks that multiply to 24: 3 × 8, 4 × 6, or 12 × 2. Ask: "can I make a 3 and an 8 out of these four numbers?"
• Try the sum shape too. 24 can also be reached by addition — e.g. 18 + 6, 16 + 8, 20 + 4 — if the cards split nicely into two groups.
• Division is the escape hatch. When no whole-number grouping works, look for the a ÷ (b − c ÷ d) shape — a small denominator made from the other cards, as in the 3 3 8 8 example above.
• Multiply by 1. Creating a fraction equal to 1 (or 0 that you add) from a pair of cards lets you "use them up" while keeping the other pair intact: a × (b ÷ b) × c needs care, but (a − b ÷ b) style constructions win hard hands.

Practice

• Play a random hand — the free game board, no signup.
• Solve a daily puzzle — one curated hand per day.
• Browse all 1,820 four-number combinations — every hand with its complete solution set.
• Generate printable worksheets — for classrooms and practice sessions.