1, 2, 3, 4
(3 + 2 + 1) x 4 = 24
There are several distinct answers. Reordering a commutative operation does not create a new answer, so 4 x (3 + 2 + 1) is equivalent to the expression shown.
math 24 game rules
Use four numbers exactly once and combine them with basic arithmetic to make 24.
See how a puzzle is solved
These examples use the same four-number rule as the game.
4, 4, 10, 10
(10 x 10 - 4) / 4 = 24
Use every card exactly once. You can work in steps: 10 x 10 = 100, 100 - 4 = 96, and 96 / 4 = 24.
1, 5, 11, 13
No solution with +, -, x, and /
Some combinations cannot reach 24 under the standard rules. Exponentiation would make a different puzzle, so it is not allowed here.
The rules in detail
- 01
Start with four card values
Ace counts as 1. Jack counts as 11, Queen as 12, and King as 13. Suits do not affect the calculation.
- 02
Combine numbers one step at a time
Choose two current numbers, choose an operation, and replace them with the result. Repeat until one number remains.
- 03
Use the standard operations
Order matters for subtraction and division. Division by zero is never allowed, and intermediate fractions are valid.
- 04
Finish at exactly 24
Do not concatenate digits or use powers, roots, factorials, or extra numbers. The final value must be 24.
What counts as a valid answer?
Can I use a fraction during a solution?
Yes. Fractions can appear in an intermediate step as long as the final value is exactly 24 and all four starting values are used once.
Can I repeat a number?
Only when that number appears on more than one card. A pair of 4 cards gives you two 4s; one card cannot be used twice.
Why does the solver show fewer answers than I found?
Some expressions are mathematically equivalent, such as changing the order of an addition. The solver groups equivalent expressions to keep the answer list useful. See the solution theory for the details.
What if there is no solution?
Some four-number sets cannot make 24 with the standard operations. You can skip the puzzle in a game or try another set in the solver.
KEEP EXPLORING
Learn more about the game
Explore solution theory, browse related sources, or start playing.