# 24 Game & Solver - Play Online and Find All Solutions

> Play the 24 game online with timer, hints and scoring, or solve any 3–6 numbers for 24 (or any target) and see every distinct solution with duplicates removed.

- URL: https://qilingtools.com/en/math/24
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Education](https://qilingtools.com/en/tags/education), [Kids](https://qilingtools.com/en/tags/kids), [Fun & Games](https://qilingtools.com/en/tags/game)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

The 24 game is the most fun way to practise arithmetic: four cards, and you combine them with +, −, × and ÷ (and brackets) to make exactly 24, using each card once. Play mode deals a random hand that’s guaranteed to be solvable — A, J, Q and K count as 1, 11, 12 and 13, or you can stick to 1–10. Tap a card, tap an operation, then tap another card to merge the two into a new card; get down to a single card worth 24 and you win. There’s a timer, a score and a streak, and if you’re stuck the one-step hint looks at the cards you have now and tells you what to work out next. Difficulty is based on how many ways a hand can be solved: easy hands have lots, hard ones have just one or need a fraction along the way. Solver mode takes any 3 to 6 whole numbers and any target, searches every expression with exact fractions, and merges answers that differ only by the order of terms, how a chain of + or × is grouped, or expanding brackets after a minus — then prints each with the fewest brackets needed. It’s been checked against all 1,820 four-card hands from 1–13: exactly 1,362 can make 24. A collection of famous hard hands — 3 3 8 8, 1 5 5 5, 3 3 7 7, 4 4 7 7 and more — is ready to try.

## How to use

1. In Play mode pick a difficulty, then tap cards and operations to merge the four cards into 24
2. Stuck? Use the one-step hint, undo, or show the answers
3. In Solver mode type any numbers and a target to list every distinct solution

## Features

- Random solvable hands, reproducible with a seed
- Difficulty from the number of solutions and whether fractions are needed
- Tap-to-merge play that works well on phones and tablets
- Timer, score, streak and one-step hints
- Solver for 3–6 numbers and any target, with exact fractions
- Equivalent expressions merged (commutative / associative), minimal brackets
- Famous hard hands: 3 3 8 8, 1 5 5 5, 3 3 7 7 and more

## FAQ

### How do you make 24 with 3 3 8 8?

8 ÷ (3 − 8 ÷ 3) = 24. First 8 ÷ 3 = 8/3, then 3 − 8/3 = 1/3, and finally 8 ÷ 1/3 = 24. It’s the most famous hard hand because the only solution goes through a fraction. 1 5 5 5 works the same way: 5 × (5 − 1 ÷ 5) = 5 × 24/5 = 24.

### When are two solutions counted as the same?

Expressions that only swap the order of terms or factors (3 × 8 vs 8 × 3), regroup a chain of additions or multiplications ((1 + 2) + 3 vs 1 + (2 + 3)), or expand brackets after a minus or divide (a − (b − c) vs a − b + c) count as one; “× 1” vs “÷ 1” and “+ 0” vs “− 0” are treated as the same too. Every expression is rewritten into a standard form before comparing, so each listed answer is genuinely different.

### How many hands can make 24?

Choosing 4 numbers from 1–13 (repeats allowed, order ignored) gives 1,820 hands, and 1,362 of them can make 24 when fractions are allowed along the way. Fewer are solvable if you only allow whole-number steps. Hands with no solution include 1 1 1 1, 1 1 1 2 and 13 13 13 13.

### Are negative numbers allowed in the middle?

By default the solver always subtracts the smaller number from the larger, so no step goes negative — that matches how children usually play, and it never makes a solvable hand look unsolvable. Tick “Allow negative intermediate results” in the solver to see those versions as well; it’s switched on automatically for a negative target.

## Related tools

- [Graphing Calculator](https://qilingtools.com/en/math/graph): Free online function graphing calculator: type sin(x), x^2 or 1/x and see the curve at once, with several functions, parametric and polar curves, PNG export.
- [Scientific Calculator](https://qilingtools.com/en/math/calculator): Free online scientific calculator: type 2*(3+4)^2, sin(pi/6) or log(8,2) and see the answer as you type, with degrees or radians and a history list.
- [Equation Solver](https://qilingtools.com/en/math/equation): Free online equation solver: enter coefficients for linear, quadratic (with discriminant, vertex and complex roots) and cubic equations, plus 2×2 systems.
- [Fraction Calculator](https://qilingtools.com/en/math/fraction): Free online fraction calculator: add, subtract, multiply and divide fractions with automatic reduction, plus fraction ↔ decimal with repeating digits.
- [Percentage Calculator](https://qilingtools.com/en/math/percentage): Free online percentage calculator: X% of Y, X as a percent of Y, increase and decrease, a value after a percentage change and the original behind it.
- [Prime Factorization](https://qilingtools.com/en/math/prime): Free online prime factorization: factor an integer with exponents, list every divisor and their sum, test primality with neighbouring primes, or list a range.
- [GCD and LCM](https://qilingtools.com/en/math/gcd-lcm): Free online GCD and LCM calculator: works with two or more integers, says whether they are coprime, shows each prime factorization and every Euclidean step.
- [Statistics Calculator](https://qilingtools.com/en/math/statistics): Free online statistics calculator: paste a data set for the mean, median, mode, range, quartiles, variance, standard deviation, standard error and outliers.