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.

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

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.

Free · No sign-up · Runs in your browserLast updated: 2026-10-26

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How to use 24 Game

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

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.