Math Cages mixes the row-and-column logic of a Latin square with a little arithmetic. Each puzzle has exactly one solution, and you can always reach it by reasoning, without guessing.
The rules
A 4×4 grid uses the numbers 1 to 4, a 5×5 grid uses 1 to 5, and so on up to 7×7.
Every row and every column must contain each number exactly once.
The grid is split into outlined cages. Each cage shows a target and an operation: “7+” means its numbers add up to 7, and “12×” means they multiply to 12.
“2−” and “3÷” cages always have two cells: the bigger number minus, or divided by, the smaller one gives the target, in either order.
A number can repeat inside a cage, as long as the copies are not in the same row or column. A one-cell cage is already filled in for you.
How to play
Tap a cell, then tap a number on the pad to place it. Tap the same number again to clear it.
The selected cell’s row and column are shaded, and matching numbers light up.
Each number key shows how many of that number are still to place.
Turn on Notes to pencil in candidates. Placing a number removes it from the notes in its row and column.
On a computer, type numbers, move with the arrow keys, press N for notes, H for a hint and Ctrl or ⌘+Z to undo.
Mistakes and hints
The game never tells you a number is wrong just because it differs from the answer. Instead it flags broken rules: a number repeated in a row or column turns red, and a full cage whose numbers miss the target gets a red label.
Stuck? Hint fills in the selected cell, or the next cell that needs one, and adds to your hint count. Undo takes back any move.
Strategy tips
Start with the most limited cages. In a 6×6 grid, “11+” in two cells can only be 5 and 6, and “3÷” can only be 1 and 3 or 2 and 6.
Big products narrow things fast: “5×” must use a 5, and in a 7×7 grid “7×” must use a 7.
A cage that fills a whole row or column must hold every number once, so its sum is fixed (10 for 4×4, 15 for 5×5, 21 for 6×6, 28 for 7×7).
When a cage is confined to one row, the numbers it needs are ruled out of the rest of that row.
Use notes for two-cell − and ÷ cages: they often have just two or three possible pairs.
Difficulty levels
Easy is 4×4, Normal is 5×5, Hard is 6×6 and Expert is 7×7, with bigger cages and fewer givens as the grid grows. Every puzzle is freshly generated and checked to have exactly one solution. Your best times are kept separately for each difficulty.