Question 5
A $2N\times2N$ board is tiled by nonoverlapping $1\times2$ dominoes. A piece visits every cell exactly once, each move going to a cell sharing a side with the preceding one. A move is called a jump if its two cells belong to the same domino. What are (a) the greatest and (b) the least possible numbers of jumps? Original weights: (a) 1 point, (b) 4 points.