Think of a number grid where every row and column uses each digit once, then add little math problems on top. Math Cage Grid unblocked splits the board into outlined cages, each labeled with a target and an operation, like 12× or 5+.
It is Simon Tatham's Keen puzzle from his Portable Puzzle Collection. Each board has one answer, and the generator builds it so you can reach that answer with reasoning instead of luck.
How to play Math Cage Grid
On a board of size N, every row and every column holds the numbers 1 to N exactly once. Cages add a second rule: the digits inside a cage must combine to the target using the shown operation.
Plus cages add up and times cages multiply out. Minus and divide clues are only used on two-square cages, and the order of the two digits does not matter. A cage of one square just tells you its number. Digits may repeat inside a cage provided they never share a row or a column.
Select a square and type its number, or right-click to jot pencil marks while you narrow things down. The Type menu changes the size and difficulty, and Custom can even switch every cage to multiplication.
Controls
| To… | 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 |
Tips
- Take the free squares. One-square cages are given answers, so fill them before anything else.
- List the combos for small cages. On a 6x6 board a 5- cage must be 1 and 6, which settles a lot quickly.
- Factor the big products. A product with a factor of 5 has to include a 5, and large products limit the options fast.
- Use row totals. Every full row adds to the same number, so a row covered by known cages except one square gives you that square.
- Fill notes, then trim. Pressing M drops every possible digit into empty squares, so you can delete candidates as you rule them out.
Math Cage Grid questions
Does 3- mean the bigger number comes first?
It works both ways. A 3- cage could hold 4 and 1 in either order, and division clues work the same way.
How do I type numbers on a tablet?
Tap a square and then tap a digit button below the grid. Switch the tap mode to pencil marks when you want notes instead of answers.
What sizes can I play?
The Type menu has small starter boards up to a big 9x9, and Custom lets you choose your own size and difficulty.
