Fill a number grid so each caged group hits its sum, product, difference or quotient, with no repeats in a row or column.
Math Cage Grid is a number puzzle that blends Latin-square logic with mental math. Bold lines split the board into outlined groups called cages. Each one carries a target number and an operation, like 12× or 7+. You write digits in every square so every cage hits its number and no line holds a duplicate.
Each board has exactly one solution, and you can always reach it with reasoning. The fun lies in narrowing the options from two directions at once.
The goal
On a board of size N, every row and every column uses the digits 1 through N once. A 6x6 board uses 1 to 6, for example.
The cages add arithmetic on top. Squares in an addition cage must total the target, and in a multiplication cage they must multiply to it. Subtraction and division only show up in cages of two squares. In those, taking the smaller digit from the larger, or dividing the larger by the smaller, must give the target. Which square holds which digit does not matter. A cage with just one square gives you its digit outright.
A cage can hold the same digit twice, provided the pair never shares a row or a column.
Entering numbers
Pick a square, then type the number you want or tap one of the buttons below the grid. To jot down candidates, right-click the square first, or press Enter to put the cursor in pencil mode. Space, Backspace or 0 clears a square.
Strategy notes
- One-square cages are free, so fill them first.
- A 5- cage on 6x6 has a single answer, the pair 1 and 6. A 2÷ cage has three choices: 1 with 2, 2 with 4, or 3 with 6.
- Break big products into factors. On any board up to 9x9, a product that is a multiple of 5 must have a 5 in it.
- Use row totals. Each row on a 6x6 board sums to 21, so if whole cages cover all but one square, subtract to get the missing digit.
- Extreme sums are tight. On 6x6, an 11+ pair has to be 5 and 6, and a 3+ pair has to be 1 and 2.
Sizes and levels
Ten presets range from an easy 4x4 to a 9x9 Normal board. The hardest setting, Unreasonable, can call for some trial and error. In Custom you can pick a grid anywhere between 3x3 and 9x9, pick from five difficulty levels, and switch every cage to multiplication for a pure factoring test. With no sums or differences to lean on, that mode makes you think hard about how factors spread across each line.
Controls
| Action | Keyboard | Mouse | Touch |
|---|---|---|---|
| Enter a digit | Arrow keys to move, then type the digit | Click a square, then type a digit | Tap a square, then tap a digit button |
| Add or remove a pencil mark | Enter switches the cursor to pencil mode, then type a digit | Right-click a square, then type a digit | Set Tap to Pencil mark (or press and hold a square), then tap a digit |
| Clear a square | Space, Backspace or 0 | — | Tap the square, then Clear |
| Fill every empty square with all pencil marks | M | — | — |
| New game, undo, redo | N, U, R | Menu buttons above the grid | Menu buttons above the grid |
Math Cage Grid FAQ
Will Math Cage Grid run on a phone or Chromebook?
Yes. On a touchscreen, tap a square and then tap a digit button under the grid. Hold a square, or set Tap to Pencil mark, to add notes instead. On a Chromebook you can click a square and type, or move with the arrow keys and type digits directly.
What is the win condition?
Every row and column must hold each digit exactly once, and every cage has to produce its number using the listed operation. When both conditions are met across the whole board, it flashes to show you have solved it.
What if I get stuck?
Press M to fill every empty square with all possible pencil marks, then strike out any candidates a cage makes impossible. Undo and redo let you back out of a wrong path. If you still can't crack it, the Solve option reveals the answer.
Is it a single-player game?
Yes. It is a solo logic puzzle with no clock. Each board has only one correct answer, so you can work at your own pace and know that the clues are enough.
