How to play the 24 Game

The 24 Game is a beautifully simple mental-arithmetic puzzle that has sharpened minds in classrooms for decades. You are handed four single digits, each from 1 to 9, and one target: make them equal 24. The catch is that you must use all four digits, each exactly once, combining them with addition, subtraction, multiplication, and division. Every puzzle here is checked to have at least one solution, so there is always an answer waiting to be found.

The goal

Build an arithmetic expression from the four given digits that works out to exactly 24. You can use +, −, ×, ÷ and as many parentheses as you need to control the order of operations.

How to play

• Tap the digit and operator buttons to build your expression, or simply type it in.
• Each of the four digits must appear once and only once — you cannot reuse a digit or glue two together into a bigger number.
• Press submit (or Enter) to check it. If it equals 24 you have solved the puzzle; if not, you will see what your expression actually came to so you can adjust.
• Stuck? The hint button reveals one valid solution, and skip moves you on to a fresh puzzle. The game keeps a running tally of how many you have solved.

Worked examples

Digits 4, 7, 8, 8: (7 − (8 ÷ 8)) × 4 = 24. Digits 8, 8, 3, 3 are famously hard: 8 ÷ (3 − 8 ÷ 3) = 24. As that second one shows, fractions are allowed along the way — only the final result has to land exactly on 24.

Strategy

The fastest route is usually to think about how 24 can be built: 3 × 8, 4 × 6, 2 × 12, or 24 + 0. Scan your four digits for a pair that already makes one of those factors, then ask what the other two digits need to become to complete it. If multiplication leads nowhere, fall back on addition — 24 is also 12 + 12, 13 + 11, or 20 + 4. And do not forget division: a tidy answer often hides behind a fraction, exactly as in the 8-8-3-3 puzzle above.