The 24 game: practising arithmetic with four numbers
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January 12, 2026
Daniel LuFull-Stack Engineer | Content Creator
Four numbers and a target of 24 leave room for quite different solutions. Fractions, brackets and working backwards make this familiar card game interesting.
Categories：Popular Science
Four numbers and a target of 24 leave room for quite different solutions. Fractions, brackets and working backwards make this familiar card game interesting.
Start with the rules
Use each of the four numbers once, with the permitted operations and brackets, to reach 24. Try familiar factors such as 3 × 8 or 4 × 6, then consider fractions. Check a proposed expression step by step.
Why 24?
Have you ever wondered why not 20 or 30? Because the number 24 is simply perfect. It has 8 factors: 1, 2, 3, 4, 6, 8, 12, and 24! This means there are many paths to reach it, and the difficulty is just right—neither too obvious nor impossible.
What Exactly Does It Train?
If you think it's just about the speed of addition, subtraction, multiplication, and division, you are underestimating it. It trains the underlying hardware of your brain.
1. Practice notes
This task asks you to hold intermediate values while trying operations. Getting more familiar with its patterns does not establish that your general memory capacity has increased.
2. Cultivating "Intuition for Numbers"
An expert sees
3, 3, 8, 8 and doesn't calculate blindly. Their intuition immediately screams: "8 divided by (3 - 8/3)".
Usually, intuition looks for 3x8 or 4x6. This ability to jump straight to the answer without logical deduction is Number Sense. It is crucial in finance, programming, and even poker.3. Practice of Reverse Thinking
Ordinary people calculate from left to right. But in this game, you need to stare at the result (24) and reverse-engineer the process. This "End in Mind" (reverse engineering) thinking pattern is key to solving many of life's problems.
Have you encountered an unsolvable hand?
Don't doubt yourself; some card combinations are indeed unsolvable! But in a standard game (using cards A-10), the probability of a solution is not 100%. If you can't solve it, don't force it; the question might just be playing tricks on you.
How Many Can You Solve Now?
Maybe your calculation speed isn't as fast as it was in elementary school, but your strategic thinking might be stronger.
No need to look for a deck of cards; we have recreated this classic mental gym for you. Not only does it generate questions, but if you really get stuck, one click will show you all possible solutions (yes, sometimes there's more than one!).
🔗 Open Make 24 Calculator
Enter your 4 numbers or generate a random hand. See if your brain is still sharp?
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Universal Formulas to Make You Look Smart
Finally, here are a few tricks for those pulling their hair out over this game:
- Use 0 and 1: If you have two identical numbers, like
5, 5, you can turn them into 1(5/5)or 0(5-5). This is very useful for assembling numbers. - Focus on 3 & 8, 4 & 6: As long as you have these numbers, see if you can make the remaining cards form their "other half."
- Don't Forget Fractions: Many legendary hard problems (like
1, 5, 5, 5) require fractions.5 * (5 - 1/5) = 24. Saying this solution out loud will definitely impress everyone.