Calcudoku

Goal

Fill the grid of n × n cells with the digits 1 to n, with no repeat in any row or column. The grid is divided into cages with thick outlines: the digits in a cage must produce the result shown in its corner using the given operation.

• +: sum of all the digits in the cage.
• ×: product of all the digits.
• −: difference between the two digits (the larger minus the smaller).
• ÷: quotient of the two digits (the larger divided by the smaller).
• A single-cell cage gives its digit directly.
• A digit may repeat within a cage, as long as it is not in the same row or the same column.

Controls

• Tap a cell, then a digit; Notes (N key) for pencil candidates, Auto notes to fill them in for you.
• Backspace or 0: erase. Arrow keys: move. Ctrl + Z: undo.

Techniques

• Combinations: a “3 ÷” cage in a 6 × 6 grid only allows 1 and 3, or 2 and 6.
• Cage and line: if every combination of a cage puts a digit in the same row, that digit is removed from the rest of the row.
• Pairs, triples, X-Wing as in Sudoku.
• At the Diabolical level, you sometimes have to assume a digit and see that it leads to a contradiction.

About the AI

The generator draws a random Latin square, cuts it into cages, picks the operations, then adjusts the layout (splitting, merging neighbouring cages) until a logical solver solves the grid using exactly the techniques of the requested level. Since every deduction the solver makes is rigorous, a grid solved from start to finish has only one solution; an exhaustive search confirms this in the tests. The same solver provides the explained hints and the Solve button.