Question 100
Let $N$ be a positive integer. A collection of $4 N^{2}$ unit tiles with two segments drawn on them as shown is assembled into a $2 N \times 2 N$ board. Tiles can be rotated.
The segments on the tiles define paths on the board. Determine the least possible number and the largest possible number of such paths.
The segments on the tiles define paths on the board. Determine the least possible number and the largest possible number of such paths.