Type in any four numbers and get every way to make 24 with +, −, ×, ÷ and brackets — including fraction and negative solutions. Free, no sign-up required.
Can these numbers make 24?
Enter four numbers from 1–13. Find ways to reach 24.
Enter your numbers to reveal the answer.
What counts as a solution
A hand counts as solved when you use all four numbers exactly once, in any order, with any combination of addition, subtraction, multiplication and division — brackets allowed. You do not need to use every operation, and you may repeat one. Decimal answers are not accepted partway through: every intermediate value must be an exact rational number, which is why a hand like 3, 3, 8, 8 still has a solution even though 3 − 8 ÷ 3 is a fraction. Expressions that are the same up to ordering or bracketing — 3 × 8 and 8 × 3 — are counted once, so the list shows every distinct way to make 24, not every way to write it down.
Worked examples
Below are hands at four levels of difficulty, each with every distinct solution. The solver gives the same output for any other four numbers you enter. Solutions marked fraction use a non-integer value partway through — they are the ones most people miss, and the ones that break solvers doing decimal arithmetic.
| Hand | Solution(s) | Type |
|---|---|---|
| 1, 2, 3, 4 | 1 × 2 × 3 × 4 | Multiple |
| 2, 3, 4, 5 | 4 × (5 + 3 − 2); 2 × (5 + 4 + 3) | Multiple |
| 2, 2, 4, 8 | 8 × 2 + 4 × 2 | Multiple |
| 2, 3, 6, 6 | 6 × 6 ÷ 3 × 2 | Multiple |
| 6, 6, 6, 6 | 6 + 6 + 6 + 6 | Multiple |
| 1, 3, 4, 6 | 6 ÷ (1 − 3 ÷ 4) | Fraction |
| 3, 3, 8, 8 | 8 ÷ (3 − 8 ÷ 3) | Fraction |
| 3, 3, 7, 7 | (3 + 3 ÷ 7) × 7 | Fraction |
| 1, 5, 5, 5 | 5 × (5 − 1 ÷ 5) | Fraction |
| 4, 4, 10, 10 | (10 × 10 − 4) ÷ 4 | Fraction |
| 1, 1, 1, 1 | No solution | Impossible |
| 2, 2, 2, 2 | No solution | Impossible |
| 1, 1, 1, 7 | No solution | Impossible |
| 1, 1, 2, 2 | No solution | Impossible |
| 5, 5, 5, 5 | 5 × 5 − 5 ÷ 5 | Multiple |
Hands that look impossible
Some hands look like they should not work, and do; others look workable and cannot be done at all.
The first group is where players give up too early. 3, 3, 8, 8 has exactly one solution and it needs a fraction — 8 ÷ (3 − 8 ÷ 3). The same trick solves 1, 3, 4, 6, 3, 3, 7, 7 and 4, 4, 10, 10. If a solver reports any of these as unsolvable, it is doing decimal arithmetic and losing the answer to rounding.
The second group is genuinely impossible. 1, 1, 1, 1 can never reach more than 4. 2, 2, 2, 2 tops out at 16. Any hand of three 1s plus a number below 8 peaks at (1 + 1 + 1) × n, which stays under 24 — that covers 1, 1, 1, 1 through 1, 1, 1, 7. When a hand is in this group the solver says so plainly, and you can be sure all 7,680 combinations were checked.
24 Game Solver FAQ
Can the solver handle fractions?
Yes. The solver works in exact fractions rather than decimals, so hands that can only be solved through a fractional intermediate step are handled correctly. Take 3, 3, 8, 8 — the only solution is 8 ÷ (3 − 8 ÷ 3) = 24. In decimal arithmetic, 3 − 8 ÷ 3 comes out as 0.333333…, and most solvers either miss this hand or report it as unsolvable. Every solution here is labelled when it needs a fraction partway through.
What algorithm does the solver use?
It enumerates every combination: all distinct orderings of your four numbers, all 64 operator assignments, and all five ways to bracket four operands. That is up to 7,680 evaluations per hand, run in your browser in well under a second. Because the arithmetic is exact, no solution is ever lost to rounding. Duplicate expressions — 3 × 8 and 8 × 3, or different bracketings of the same additions — are collapsed before the results are shown.
Is there a 24 game solver app?
You do not need one. This solver runs in the browser on any phone, tablet or desktop, with no download and no install. It is built mobile-first: the input row and the answer list are sized for a phone screen, so you can type four numbers and read the solutions without pinching or scrolling sideways. Add the page to your home screen if you want one-tap access.
Why does my hand have no solution?
Some hands genuinely cannot make 24, no matter how you combine them — 1, 1, 1, 1 is the simplest example, since the largest value you can reach is 4. When the solver finds nothing, it says so plainly instead of showing a blank result, and you can be sure every combination was checked. If you are playing with physical cards, check that you entered the numbers correctly first.
Can it solve 3 numbers instead of 4?
This solver uses four numbers, which is the standard 24 Game format. Enter four operands and combine them with any mix of addition, subtraction, multiplication and division, with brackets allowed. Four-number hands remain the default because they provide the full game challenge.
How many solutions does a hand have?
It varies a lot. Most hands have several solutions once you collapse expressions that are the same up to commutativity — 2, 3, 4, 5 works as 4 × (5 + 3 − 2) and as 2 × (5 + 4 + 3), among others. A few hands have exactly one essential solution: 3, 3, 8, 8 is the classic case, and it is 8 ÷ (3 − 8 ÷ 3). The solver lists every distinct solution and marks the ones that need a fraction.
Is the solver free? Do I need to sign up?
Free, and no account is needed. Type your four numbers and the solutions appear straight away — nothing is behind a login, a paywall or a "view more" click. The solver runs entirely in your browser, so nothing is uploaded and there is no per-day limit. If you use it regularly, bookmarking the page is the only thing worth doing.
Can teachers use the solver in class?
Yes, and it is designed for it. The solver is ad-supported rather than paid, works on classroom tablets and Chromebooks with no install, and shows every solution rather than just the first — which makes it useful for comparing a class's answers against the full list. For printed material, the free printable cards and answer keys on our 24 game cards page cover the same range of difficulty.