a) A rook in chess can move any number of squares in the same row or column. Let’s invent a new figure, a “little rook” that can only move one square in each of these directions. If we start with a “little rook” in the bottom right corner of an \(8 \times 8\) chessboard, can we make it to the opposite corner while visiting each square exactly once?
b) A king in chess moves like the “little rook”, but he can also move one square along a diagonal. Can we do the same task with a king?