24 Game — Play the 24 Card Maths Puzzle

What this level trains

The 24 game is a maths puzzle with one goal: take four numbers and combine them with addition, subtraction, multiplication and division, using each card exactly once, to reach 24. Most four-card hands have a solution, but finding it means trying a few routes before one works out.

Difficulty comes from the solution structure rather than from big numbers. The easy end is anchor warm-ups such as building 6×4 or 8×3; the hard end needs unique solutions and counter-intuitive intermediate values that pass through fractions or negatives before finally landing on 24.

You solve each puzzle by dragging one card onto another and choosing an operator, merging two cards into a single result. Four cards collapse to one in exactly three merges, and every intermediate value stays visible, so the game trains choosing between paths as much as raw calculating.

Each set holds five puzzles mixed from easy to hard, and one hint per set reveals the correct first step at a cost of 20 percent on the final score. The levels also raise the per-puzzle benchmark, from about 10 seconds at level 1 to a full minute at level 8.

How to play

1. Read the cardsEach puzzle deals four cards. A counts as 1, and J, Q and K count as 11, 12 and 13, so the four numbers you work with are already set.
2. Merge two at a timeDrag one card onto another and pick plus, minus, times or divide; the two cards become one result card. Intermediate results may be fractions or negative numbers, not only whole numbers.
3. Use exactly three mergesTurning four cards into one takes exactly three operations, and every card must be used exactly once. That rule is why a puzzle with no solution cannot be forced.
4. Solve and scoreWhen one card remains and equals 24, the next puzzle starts automatically. You may request one hint per set, which reveals the correct first step but scores the whole set at 80 percent.

8 difficulty levels and score thresholds

The eight levels are defined by the difficulty tiers of the five puzzles in a set. Level 1 is all anchor warm-ups, while level 8 mixes unique solutions, counter-intuitive intermediates and top-tier puzzles that require nested fractions. The excellent threshold for a set is the sum of the five per-puzzle benchmarks plus four puzzle-switch overheads, with good at 1.3 times that and pass at 1.8 times; using a hint multiplies the final score by 80 percent.

You can only reach the maximum score at or under the full-mark line. Past the pass line the score keeps decaying, down to 0 at twice the pass line. The maximum rises from 3000 to 10000 across the levels.

Tips and common mistakes

• Start from anchors24 equals 3×8, 4×6, 12×2, 25−1 and many more. If the cards can build one of these pairs, lock it in and the remaining cards narrow down quickly.
• Allow fractions in the middleMany impossible-looking puzzles actually run through paths such as (3 − 8÷3) × 9. A third appearing midway is normal, so do not abandon a route just because it turned fractional.
• Do not fear negativesA negative intermediate value is often the only road to 24, for example 6 ÷ (1 − 3/4). Treat it as a clue rather than a dead end.
• Work backwardsAssume the last step adds two intermediate results to 24, then ask whether the four cards can split into two groups that each build one of those numbers.

Frequently asked questions

Does every 24 game hand have a solution?

No. Among the 1,820 four-card combinations drawn from A to K with repetition allowed, most are solvable but some are not, such as four aces. Every puzzle on this site is checked by a solver, so it is guaranteed to have a solution, and the top levels guarantee a unique solution or require fractions.

Can each card be used more than once?

No. All four cards must be used, and each exactly once. That is really the same rule as collapsing four cards into one with exactly three merges, and thinking of it as three merges is the easiest way to check that a solution is valid.

Are decimals and negative numbers allowed?

Yes. Intermediate values may be any rational number; only the final result must equal 24. Allowing fractions and negatives is precisely what makes the harder levels of the 24 game interesting, and those maze-like mid values are the whole point.

Does a hint cost points?

Yes. A set that used a hint is scored at 80 percent, because the hint reveals the correct first step and removes the main part of the search for the solution. If you want a clean, comparable score, try to solve the set without it.

How long is one set?

A set is five puzzles. At low difficulty each puzzle takes tens of seconds, while a top-level puzzle can take several minutes, and the time thresholds are built from the puzzle count and the merge cost of each puzzle.

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