## Knights and Queens

**Goal:**

Among the famous chess inspired mathematical puzzles are those of the Knight's Tour and the Eight Queens. You can consult
the corresponding wikipedia pages on the Knights and the Queens.

It is possible to make many variations of these puzzles. For instance, we will ask to find the shortest path for a knight to jump from one square
to another one. Of course, we shall not do this only on the usual 8x8 chess board, but on arbitrary chess boards, not necessarily square ones.
We shall actually go to three dimensions (or even n if we are daring); we could allow a three-dimensional knight to jump a distance of 3 in one direction (e.g. along the x-axis), a distance of 2 in another direction (e.g. the y-axis) and a distance of 1 in the last direction.

The goal is to program these (and other) variations, illustrate them and make observations (for instance, on the (im)possibility for certain paths, the minimal length of paths, etc.).

**Supervisors:**
Gabor Wiese, George Kerchev

**Difficulty level:**
Any.

**Tools:**

- Any programming language or any Computer Algebra System such as sagemath
- Image processing software