Use all four numbers exactly once with addition, subtraction, multiplication and division to make 24. Every hand is checked by the built-in solver, so a solution always exists.
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Tap a number, then an operation, then another number. Keep combining until one card shows 24.
Keyboard: 1–4 pick a card, +-*/ operations, Backspace undo, N new hand.
Enter four numbers (whole numbers 0–999) and press Solve to see every distinct way to reach the target.
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How to use the 24 Game
Pick a difficulty: Easy, Normal or Hard. A new solvable hand is dealt at once.
Tap a number card, then an operation (+ − × ÷), then a second card. The two cards merge into their result.
Keep combining until one card is left. If it shows 24 you win; otherwise press Undo step or Reset hand.
Stuck? Press Show solution (it resets your streak) or New hand to skip.
Use the Solver tab to enter any four numbers and a target and list every distinct solution.
How to think about a 24 hand
Almost every solution ends with one of a handful of final steps. Instead of trying random combinations, look for a way to build one of these pairs from your four numbers:
Final step
What to look for
Example hand → solution
3 × 8
A 3 (or a way to make 3) and the other numbers making 8
3, 4, 6, 10 → 3 × (10 + 4 − 6)
4 × 6
A 4 or a 6, and the rest making its partner
2, 3, 4, 5 → 4 × (5 + 3 − 2)
2 × 12
Two or three numbers making 12, the rest making 2
1, 2, 5, 7 → 2 × (7 + 5) × 1
20 + 4, 25 − 1
A product near 24, then add or subtract the leftovers
A promising idea often uses only three of the numbers. Then you have to fit the fourth in without changing the value: multiply or divide by 1, build one factor out of two numbers, or add one number and subtract another. When you are stuck, Show solution reveals the cleanest answers for the current hand.
Famous hard hands
Hand
Solution
Why it is tricky
3, 3, 8, 8
8 ÷ (3 − 8 ÷ 3)
Only solution, and it passes through 1/3
1, 5, 5, 5
5 × (5 − 1 ÷ 5)
Needs 24/5 as a middle step
3, 3, 7, 7
7 × (3 + 3 ÷ 7)
Needs 24/7 as a middle step
1, 3, 4, 6
6 ÷ (1 − 3 ÷ 4)
Dividing by the fraction 1/4
4, 4, 10, 10
(10 × 10 − 4) ÷ 4
Builds 96 first, then divides
Tips for faster solving
Learn the factor pairs of 24: 1 × 24, 2 × 12, 3 × 8 and 4 × 6. Most answers finish with one of them.
Use a 1 as a "free" number: multiplying or dividing by 1 never changes the result, and 1 can also add or subtract to nudge 23 or 25.
Pairs that cancel: two equal numbers can make 0 (x − x) or 1 (x ÷ x), which lets you absorb a number you do not need.
Think in fractions on Hard: if nothing works with whole numbers, try dividing a small number by another to get a fraction, then multiply back up.
Frequently asked questions
What are the rules of the 24 game?
You get four numbers and must use each one exactly once, together with addition, subtraction, multiplication and division, to reach 24. You can group operations in any order (that is what parentheses do). Joining digits into a two-digit number, powers and square roots are not allowed in the standard game.
Does every set of four numbers have a solution?
No. With numbers from 1 to 13 there are 1,820 different hands (ignoring order), and 1,362 of them can make 24. Sets like 1, 1, 1, 1 or 1, 1, 1, 2 are impossible. This game only deals hands that its solver has confirmed are solvable.
What is the hardest 24 game hand?
Hands that need a fraction along the way are usually the hardest, because most people only try whole numbers. Classic examples are 3, 3, 8, 8 (8 ÷ (3 − 8 ÷ 3) = 24), 1, 5, 5, 5 (5 × (5 − 1 ÷ 5) = 24) and 3, 3, 7, 7 (7 × (3 + 3 ÷ 7) = 24).
How does the solver count distinct solutions?
It tries every way to combine the numbers with the four operations, then treats answers that differ only by swapping the order of an addition or multiplication, or by regrouping a chain such as a + b + c, as the same solution. That way 8 × 3 × 1 × 1 and 1 × 1 × 3 × 8 are counted once.
Can I use the solver for targets other than 24?
Yes. In the Solver tab you can enter any four whole numbers from 0 to 999 and any whole-number target, for example to make 10 or 100 from four numbers.
What do the difficulty levels mean?
Easy uses only the numbers 1 to 9 and deals hands with at least four distinct solutions, including one that stays in whole numbers. Normal uses 1 to 13 (like a deck of cards with jack, queen and king as 11, 12 and 13). Hard deals hands with at most two distinct solutions or ones that can only be solved with a fraction.
Is the 24 game good for learning math?
Yes. It builds mental arithmetic, number sense and an intuition for the order of operations and for factors of 24 (1×24, 2×12, 3×8, 4×6). Teachers often use it as a warm-up from about age eight; Easy mode is a good starting point.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.