Chain Sudoku

The name "Strimko" is trademarked by the Grabarchuk family, who claims to have developed this sudoku variant.

An unsolved puzzle consists of a square grid. The cells are further interconnected into groups, such that there are <em>n</em> groups ("chains") of <em>n</em> cells each. Some of the cells have been filled in.

The goal is to fill in all the cells so as to create a Latin Square.

The solved grid must satisfy the following conditions:

Strimko