How to play
Math Cages mixes two ideas: a Latin square, like the rows and columns of a sudoku, and small sums you have to make come out right. The grid starts completely empty. There are no given digits; everything you need is in the cage clues.
The square. On a grid of size n, every row and every column holds each digit from 1 to n exactly once. Difficulty sets the size: Easy is 4×4, Medium 5×5 and Hard 6×6.
The cages. Bold outlines split the grid into groups of cells. The top-left cell of each cage shows a target and an operation:
- +: the cage’s digits add up to the target.
- ×: they multiply to the target.
- −: a two-cell cage whose larger digit minus the smaller equals the target.
- ÷: a two-cell cage whose larger digit divided by the smaller equals the target.
- A lone number with no sign marks a one-cell cage: that cell simply holds the number.
Subtraction and division only appear on two-cell cages, so order never matters: 3− can be 1 and 4 or 4 and 1. Bigger cages (up to three cells on Easy, four on Medium and Hard) always use + or ×.
Entering digits. Tap a cell and pick a digit, or type it on the keyboard; arrow keys move around and Backspace or Delete clears. Undo steps back. If a digit repeats in a row or column, those cells are flagged, and once a cage is full but misses its target, its cells are flagged too. The clock runs in the bar, and New puzzle creates a fresh grid at the current difficulty.
How the puzzles are built
Each puzzle starts from a random valid Latin square. The grid is carved into cages, and each cage gets an operation and the target its digits produce. Then a solver checks for a second solution. If one exists, the cage where the two answers disagree is split, and that cell becomes a one-cell cage. This repeats until exactly one solution remains, so every puzzle can be solved by reasoning alone, with no guessing needed.
That last step is also why some grids give you more single-number cages than others: those are cells that were needed to rule out a rival solution.
Strategy
Fill the free cells first. One-cell cages are given digits in disguise. Write them in, then cross that digit out of the rest of its row and column in your head.
Read the two-cell cages for pairs. On a 6×6 grid, 5− can only be 1 and 6. 3÷ means 1 and 3 or 2 and 6. 2÷ allows three pairs (1-2, 2-4, 3-6). The fewer pairs a clue allows, the sooner you should look at it.
Factor the products. A product tells you a lot because primes can’t hide. On a 4×4 grid, a two-cell 6× must be 2 and 3, since there is no 6 to pair with a 1. On a 6×6 grid, any product that is a multiple of 5 must contain the 5, and 12× in two cells is either 2 and 6 or 3 and 4.
Use the row totals. Every row and column of a 4×4 grid sums to 10 and multiplies to 24. For 5×5 it is 15 and 120, and for 6×6 it is 21 and 720. When cages cover a whole row except for one or two cells, the missing amount tells you what’s left.
Remember that cages can repeat digits. A bent three-cell cage spans two rows and two columns, so the same digit can appear twice in it as long as the two copies don’t share a row or column. In an L of three cells, only the two end cells can match, so 9+ there might be 4, 1 and 4 with the 1 in the corner.
Work in pairs of lines. If two cells in a row are locked to 2 and 4 by a cage, no other cell in that row can be 2 or 4. This “pair” logic, borrowed from sudoku, does most of the work on Hard grids.
If you like the row-and-column logic without arithmetic, Sudoku is the obvious next stop, and Kakuro is the crossword-style puzzle built entirely on sums.
If you enjoy Math Cages, try Minesweeper or Nonogram next.
