Math Cage Puzzle

Fill the grid with the numbers 1 to n so that no number repeats in any row or column. Each outlined cage shows a target and an operation: the numbers inside must make that target. In a cage marked 6×, the numbers multiply to 6.

How to play

1. Tap a square, then tap a number (or type it). Arrow keys move around.
2. Each row and each column must contain every number from 1 to n exactly once.
3. The numbers in each cage must combine to the target with the cage’s operation. In − and ÷ cages (always two squares), subtract or divide the smaller number from the larger one. A cage with one square just shows its number.
4. Press Check to see mistakes. The puzzle is solved when every rule works.

Solving strategies

• Single squares first: a one-square cage gives a free number.
• Factor the × cages: 12× in two squares of a 4×4 must be 3 and 4.
• Use the row sum: each row of a 4×4 adds to 1 + 2 + 3 + 4 = 10; of a 6×6, to 21.
• − cages with big targets: 3− in a 4×4 must be 1 and 4.
• ÷ cages: 2÷ means one number is double the other: 1 & 2, 2 & 4 or 3 & 6.

Why these puzzles build math skill

Each cage is a small equation with unknowns, so solving means listing factor pairs, sums and differences and ruling out options. Players practice number facts, logical deduction and the idea of a Latin square: a grid where every symbol appears once per row and column.

Cage puzzle logic quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

Is this the same as KenKen?

It follows the same kind of rules as KenKen-style puzzles: a Latin square with arithmetic cages. These puzzles are generated fresh each time.

Does every puzzle have exactly one solution?

Not always: some random puzzles allow more than one answer. Any grid that follows every rule is accepted as solved.

What do − and ÷ mean in a cage?

Take the larger number minus (or divided by) the smaller one. These cages always have two squares.

Can numbers repeat inside a cage?

Yes, if the repeated squares are in different rows and columns, as can happen in an L-shaped cage.

Which size should I start with?

Start with 4 × 4 to learn the logic, then move up to 5 × 5 and 6 × 6.

Sources

• Wolfram MathWorld: Latin Square

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