Logic Masters Deutschland e.V.

This is a variant of a calcudoku (also known as KenKen or TomTom) puzzle, in which the values of cages are not shown. Only the kropki relationships between them are given.

Fill the grid with digits from 1 to 9, so that every row and column contains each digit exactly once.

Each cage indicated by the thick lines shows an arithmetic operation, either +, –, x, or /. The 'value' of the cage is obtained by applying the operation to the digits in the cage. For subtraction and division cages, which in this puzzle have exactly 2 cells, the value is A–B or A/B where A is the larger digit and B is the smaller digit in the cage.

Digits may repeat within a cage.

All cage values, including those of division cages, are positive integers.

A white dot between 2 orthogonally adjacent cages means that the cage values differ by 1. A black dot means that the cage values are in a 1 to 2 ratio. All possible dots are shown.

The location of a dot along the boundary between 2 cages is irrelevant. No relation is implied between the digits in the cells that touch the dot.

The puzzle is available on Penpa.