Karl Scherer made the interesting Squared Chain Puzzle. Start with a $7\times7$ board, with a queen somewhere. Make a legal move with the queen, placing coins over all squares visited. For subsequent moves:
- No squares can be revisited.
- Each move must move through +1 or -1 spaces.
There is a known solution for visiting all squares in 28 moves. Is that the best? With 10 moves, I can visit all but 8 squares. Is that the most possible? What is the highest number of squares that can be visited with 11, 12, 13, 14 moves? How do the answers change for larger square boards or rectangular boards?
