MiniZinc solution to the first step of the "Christmas GCHQ Puzzle":

The constraints:

It is similar to the Sudoku puzzle, with a little bit more complex vertical/horizontal constraints.

• The first constraint is for the "fixed" cells to be in place
• The other two (almost identical) groups of horizontal/vertical constraints ensure that:
• The provided intervals have 1's all along
• Every interval (except of the first one) has a preceding 0 AND the intervals do not overlap
• The total amount in 1's in every row/column is the same as the sum of the provided intervals' lengths

The puzzle itself:

In this type of grid-shading puzzle, each square is either black or white. Some of the black squares have already been filled in for you. Each row or column is labelled with a string of numbers. The numbers indicate the length of all consecutive runs of black squares, and are displayed in the order that the runs appear in that line. For example, a label "2 1 6" indicates sets of two, one and six black squares, each of which will have at least one white square separating them.”