Logische puzzel

A logic grid puzzle (logische puzzel) with three categories, like "which child
has which pet, and which colour do they like?". The booklet prints the clues;
the answer sheet has the grid, so pupils puzzle on the sheet and not in their
booklet. The grid is like a puzzle book's: the second and third category
across, the first and third down. Pupils colour a cell in when two items go
together and put a cross in it when they don't. The two boxes with the first
category are the answer: the scanner reads each of their cells as coloured in
or not, and each right match is a point. The third box is scrap.

Each clue has its printed `text` and the `facts` it states, as pairs of items:
`{ is: [Anna, kat] }` or `{ not: [Anna, hond] }`. Validation checks each fact
against the `key`, and that the facts alone lead to the whole answer with the
rules of the grid (a coloured-in cell crosses out the rest of its row and
column; the last empty cell gets coloured in; two boxes together give the
third). So a puzzle that
needs guessing is an error: add a clue, or let one say more. Item names are
how facts and the key refer to items, so they are unique across categories.

For groep 5-6, three items per category is plenty; four makes it a real
puzzle. Mix clues that say what is (`is`) with ones that say what isn't
(`not`), and let at least one step need two boxes together (`link`).

Add a `solution` too: the cells in the order a pupil fills them, each with
its rule; `mark: check` colours a cell in, `mark: cross` crosses it out.
Colouring in crosses out the rest of its row and column in that box by
itself, as a pupil does right away, so those crosses are no moves of their
own. Go on until the whole grid is filled in, the third box too: the teacher
view ends on the full grid. The teacher manual shows it step by step, the
teacher view plays it on the grid one move at a time, and the booklet's
hints sheet gets a hint for the start and for each point where the clues
give nothing new.