Enter four numbers and this 24 game solver will search all valid arithmetic expressions using +, -, ×, and ÷ to reach your target (default: 24).
What is a Math 24 calculator?
A Math 24 calculator (also called a 24 game solver) takes four numbers and finds arithmetic expressions that evaluate to 24. It is popular with students, teachers, puzzle fans, and anyone who wants quick arithmetic practice without using a long worksheet.
The classic puzzle rules are simple: use each of the four numbers exactly once, combine them with basic operations, and hit the target. Most versions allow parentheses to change operation order, which is where the puzzle becomes interesting.
How this 24 game solver works
1) Tries every possible number order
The tool checks all permutations of your four inputs. For example, 1, 3, 4, 6 can be arranged in 24 different ways, and each order can produce different valid expressions.
2) Tries every operator combination
For each number order, it tests combinations of +, -, *, and /.
3) Tries all major parenthesis patterns
Parentheses determine operation sequence. This page checks the common binary expression structures, such as ((a op b) op c) op d and (a op b) op (c op d), to avoid missing solutions.
4) Filters duplicates and near-equal floating-point results
Because division can create decimals, the solver uses a small tolerance when comparing to the target. It also removes duplicate equivalent expressions from the final result list.
Tips for solving 24 faster by hand
- Look for multiplication anchors: 24 is highly factorable (1×24, 2×12, 3×8, 4×6).
- Use division to create missing factors: for example, turning 8 and 4 into 2 if you need a 12 from 6×2.
- Pair numbers first: try two small sub-results, then combine.
- Think in reverse: ask “What should happen right before 24?” (like ×3, ×4, +6, etc.).
Example puzzles
- 4, 7, 8, 8 →
(7 - (8 / 8)) * 4 = 24 - 1, 3, 4, 6 →
6 / (1 - (3 / 4)) = 24 - 2, 2, 6, 6 →
(6 + 6) * (2 / 2) = 12(not 24, good example of a near miss)
FAQ
Can I use decimals or negative numbers?
Yes. This calculator accepts any numeric input, not only integer cards.
Why does “show all solutions” sometimes return many answers?
Some number sets are rich in symmetry, so many valid expressions collapse to 24. The solver reports unique expression strings and avoids exact duplicates.
Is this useful for teaching?
Absolutely. Teachers can use it to generate puzzle sets, validate student answers, and demonstrate order of operations with instant feedback.