Exercise 6.13 (Knight on the Chess Board). Place a knight on any selected field of the chessboard 6 × 6 and find a path of the knight that returns to the selected field and uses other fields only once. If not all fields are used then repeat the same procedure starting form a new unused field.

Finally all fields must be used.

1 Is there a set of paths of the knight where each path uses all the other fields of the board exactly once and returns to the selected start field?

2 How many Boolean variables are necessary to model this problem?

3 Find and explain a Boolean model for this problem.

4 Generate a PRP in order to solve the problem. Due to the marginal overlapping of the generated TVLs, the order of the required intersections is essential. Find an appropriate order using the XBOOLE Monitor. How many solutions exist?