24 game solver facts at a glance
The 24 game solver takes any four whole numbers, tries every order, every pairing and all four operations with exact fractions, and lists each different answer. It is free, needs no account and runs in your browser.
| Numbers | Four whole numbers from 0 to 99, or cards A, 2 to 10, J, Q, K |
|---|---|
| Operations | Add, subtract, multiply and divide, each number used exactly once, any grouping |
| Fractions | Allowed along the way, as in 8 ÷ (3 − 8 ÷ 3); kept exact, never rounded |
| Negative numbers | Not used along the way: every subtraction takes the smaller number from the bigger |
| Same answer | Answers that differ only in order, grouping, or multiplying by 1 count once |
| Hands from 1 to 13 | 1,820 different hands, 1,362 can make 24 and 458 cannot |
| Hands from 1 to 9 | 495 different hands, 404 can make 24 and 91 cannot |
| Other targets | Any whole number from 0 to 999 |
| Price and setup | Free, no account, no download; runs in your browser |
How to use the 24 game solver
Type the four numbers of your hand, press Solve and read the answers: the simplest one comes first, with its steps below.
- Type the four numbers. Use the numbers on your card, or the values of four playing cards: A is 1, J is 11, Q is 12, K is 13.
- Press Solve. The solver tries every way to pair the numbers with +, −, × and ÷ until one number is left.
- Read the answers. Each line is a different answer that equals 24. Answers with whole numbers only come before answers that need a fraction.
- Follow the steps. Tap any answer to see it as steps, such as 8 ÷ 8 = 1, then 7 − 1 = 6, then 6 × 4 = 24.
- Keep or share it. Copy all answers as text, or copy a link that reopens this hand and solves it.
The rules of the 24 game
You get four numbers, from a card or from four playing cards. Use each number exactly once, with addition, subtraction, multiplication and division, and make 24. You may use parentheses to choose the order. You may not glue digits together, so 1 and 2 cannot become 12, and you may not use powers or square roots. With playing cards, aces count as 1 and jacks, queens and kings as 11, 12 and 13, or some players take the face cards out and play with 1 to 10 only.
Most hands have a quick answer once you look for a pair that makes 24 with a third number: 3 × 8, 4 × 6, 2 × 12, or 24 + 0. In 4 7 8 8, 8 ÷ 8 is 1, 7 − 1 is 6, and 6 × 4 is 24.
Hard 24 game hands that need fractions
A few hands can only make 24 by passing through a fraction. Of the 1,362 hands from 1 to 13 that can make 24, 16 need one, and they are the famous hard hands. The best known is 3 3 8 8: 8 ÷ 3 is 8/3, 3 − 8/3 is 1/3, and 8 ÷ 1/3 is 24. Others are 1 5 5 5, which is 5 × (5 − 1 ÷ 5), and 1 3 4 6, which is 6 ÷ (1 − 3 ÷ 4). If you are stuck on a hand that looks impossible, try dividing to make a small fraction and then dividing by it.
Which 24 game hands cannot be solved?
With numbers from 1 to 13 there are 1,820 different hands, counting 1 2 3 4 and 4 3 2 1 as the same. 458 of them cannot make 24 at all, such as 1 1 1 1, 1 1 1 2 and 13 13 13 13. With 1 to 9 only, 91 of 495 hands have no answer. The solver says so plainly when a hand has no answer, so you know it is not you. Every hand dealt in the game on this page has at least one answer.
How the solver works
The solver picks two of the numbers, combines them with one of the six possible moves (a + b, a × b, a − b, b − a, a ÷ b, b ÷ a), and repeats with the three numbers left, then the two left, until one number remains. It keeps the answers that equal the target. All values are exact fractions, so nothing is lost to rounding. To group answers that are really the same, it writes each one as a sorted list of added and subtracted parts and multiplied and divided parts; 1 + (2 + 3) and (3 + 2) + 1 become the same list.
Frequently asked questions
Can every 24 game hand be solved?
No. With numbers from 1 to 13 there are 1,820 different hands and 458 of them cannot make 24, such as 1 1 1 1. With numbers from 1 to 9, 91 of the 495 hands cannot. The solver tells you when a hand has no answer.
Does the solver use fractions?
Yes, when a hand needs them. Numbers stay exact, so 8 ÷ (3 − 8 ÷ 3) is found for 3 3 8 8. Answers with whole numbers only are listed first, and a note marks the ones that pass through a fraction.
What do aces and face cards count as?
Type A for 1, J for 11, Q for 12 and K for 13. If your group plays with face cards as 10, type 10 instead.
Why are some answers missing, like the same one in a different order?
Answers that differ only in the order of adding or multiplying, in grouping, or in multiplying or dividing by 1 are counted once, so 1 × 2 × 3 × 4 and 4 × 3 × 2 × 1 are one answer. The solver also never goes below zero along the way.
Can I make a number other than 24?
Yes. Open Aim for a number other than 24 and type any whole number from 0 to 999. The game on this page always aims for 24.
Is the 24 game solver free?
Yes. It is free, with no account and no download, and it runs in your browser. A hand link keeps the four numbers in the link itself.