Twenty-Four Card Game — 24 Game Solver & Trainer

The Twenty-Four card game — usually called simply the 24 game — is a fast math card game that likely started in Shanghai, China in the 1960s. Flip four cards and use each one exactly once, with + − × ÷ and parentheses, to make 24. Train with a 60-second timer below, or use the free 24 game solver to see the solution for any four cards. Runs 100% locally in your browser — no ads, no signup.

Time 60s

Can you make 24 with these four cards?

24 Game Solver

Type any four numbers from 1 to 10 and the solver finds every way to make 24 using each number exactly once.

How to Play the 24 Card Game

Deal four cards from a 40-card deck (A–10 only; face cards removed, A = 1).
Use all four numbers exactly once, in any order.
Combine them with + − × ÷ and parentheses to make exactly 24. Example: 5, 7, 8, 9 → 8 × 5 − (7 + 9) = 24.
First to a solution wins the set in the traditional 2-player race; here, beat the 60-second timer instead.

Example

You flip 5 7 8 9. One way to 24:

Multiply 8 × 5 → 40
Add 7 + 9 → 16
Subtract: 40 − 16 → 24 ✓ (that is 8×5 − (7+9))

Every number was used exactly once — that is all the game asks. Now try 1 1 1 1: no matter how you combine them, you cannot reach 24. Roughly 20% of hands are unsolvable like this; the solver on this page tells you instantly.

Tips for Making 24

Look for factors first — 24 = 6 × 4, 8 × 3, 12 × 2, 24 × 1. If you can make one factor from two cards and the other from the remaining two, you're done.
Try addition targets — 24 = 20 + 4, 16 + 8, 15 + 9: sometimes a sum is easier to spot than a product.
Use division sparingly — a ÷ b only helps when a is an exact multiple of b (e.g. 8 ÷ 2 = 4).
Check for 0 and 1 tricks — X + 0 = X and X × 1 = X are hidden helpers.
Roughly 80% of four-card sets are solvable — if you're stuck for a long time, it may be one of the unsolvable 20%.

FAQ

What is the 24 game?

The 24 game is a mental-math card game: four cards are shown, and you must combine their values with + − × ÷ and parentheses so that the result is exactly 24, using each card once. It's popular in classrooms worldwide as a fast arithmetic drill.

Is the 24 game really from China?

According to Denexa Games' rules documentation, Twenty-Four likely originated in Shanghai, China in the 1960s and spread to other Chinese cities and abroad from there. It is often listed among Chinese card games.

Which cards do you use for the 24 game?

A standard deck with the J, Q, K removed — a 40-card deck of aces (worth 1) through 10s in all four suits. The suits themselves don't matter, only the numbers.

Is every set of four cards solvable?

No. For four distinct numbers from 1–10, roughly 80% of combinations have at least one solution. The solver on this page tells you immediately whether your set has one.

How does the 24 game solver work?

It exhaustively tries every way to pick two numbers, combine them with one of the six operations (a+b, a−b, b−a, a×b, a÷b, b÷a), and repeat until one number remains. It runs instantly in your browser — nothing is sent to a server.

Do I need an account or a download?

No. The trainer and the solver run entirely in your browser and work offline. No ads, no signup, no data collection.

📖 Rule Source — where these rules come from

Source	Rules as documented by Denexa Games, "Twenty-Four" (2017), describing the game's probable origin in Shanghai, China in the 1960s.
Original Rules	2 players each flip two cards from a 40-card deck (A–10, no face cards). Both race to combine all four values with + − × ÷ (parentheses allowed) to reach exactly 24. First to slap the table and state a correct solution wins the set; a wrong answer loses it. Unmatched sets may be swapped one card at a time.
Regional Names	二十四点 (Èrshísì Diǎn) · Twenty-Four · The 24 Game · Make 24
Single-Player Adaptation	The two-player race is replaced with a 60-second solo timer and a Reveal button that shows one solution from the built-in solver.
Win Rate / Target	Not recorded in sources. Solo target: solve within 60 seconds (about 80% of sets are solvable).
Implementation Notes	Solver enumerates all binary-operation trees over the four values and deduplicates results. Float comparisons use a small epsilon. The 4-player variant and the swap-rule are omitted.