prize13-4, Exercise 3: Counting moves

Model answer (check the details):

Using the script from the chapter:

    print(len(old_queen(0, 0)), len(new_queen(0, 0)))   # 1 and 21
    print(len(old_queen(3, 3)), len(new_queen(3, 3)))   # 4 and 27

From the corner (0, 0) the old counsellor has only one move (the single diagonal square), while the new queen reaches 21 squares: 7 along the rank, 7 along the file and 7 along the diagonal.

From the centre (3, 3) the old piece has 4 moves (the four diagonal neighbours) and the new queen has 27: 14 along the rank and file together, and 13 along the two diagonals.

The old piece is weak everywhere and cannot control distant squares; the new queen is strong even in a corner and much stronger in the centre. That difference is why the game became fast and tactical.

Care: these counts are for an empty board; other pieces reduce the number in a real game.