Answer to Question #93771 in Discrete Mathematics for Ruby

Question

In a game of chess, a queen can travel any number of squares in a straight line- horizontally, vertically or diagonally. Moving the queen from queen (q) to king (k) visiting each square exactly once with the minimum number of moves possible

Answer 1

Diagonal moves are obviously impractical, because the diagonal move captures a small number of cells, and also blocks the path of future lines. Since the beginning and end cells are on the same horizontal, it is optimal to fill the horizontal completely, using vertical single-celled transitions. Use a large one vertical line to climb up and 7 small ones to make transitions from horizontal to horizontal. There are 8 horizontal lines in total, but since it is impossible to draw one horizontal line through the entrance and exit, at the bottom it will be divided into two parts, that is, 9 horizontal lines. 1+7+9=17 moves only. Let's show one of the options: