A compact number-logic puzzle: fill every cage with consecutive numbers so that no two equal numbers ever touch, not even on a diagonal.
The grid is split into bordered regions, or cages. Fill each cage with the numbers 1 up to its size, a four-cell cage uses 1 to 4, a five-cell cage uses 1 to 5, and so on. Every number appears exactly once per cage.
The twist: no two equal numbers may sit in neighbouring cells, including diagonally adjacent ones. A handful of cells are given to start; the rest is yours to deduce. Solve the whole grid without conflicts to win.
The structure belongs to the region-filling family — the same idea as killer sudoku, where bordered cages constrain what can go inside them, resting on the mathematics of the Latin square.
The specific rules — fill each cage with 1 up to its size, and forbid equal numbers from touching even diagonally — circulate internationally under the names Suguru and Tectonic.
What the diagonal no-touch rule buys is deduction without arithmetic. Killer sudoku leans on cage sums; here there is nothing to add up, so every inference is positional, which makes the puzzles solvable by pure reasoning at sizes far smaller than a sudoku needs.
Cagefive is a free browser version of the classic region-filling number puzzle published internationally as Suguru and Tectonic: fill each cage with 1 up to its size, and never let two equal numbers touch, even diagonally. Solvable by pure deduction, with daily challenges and three sizes, no download or sign-up.