Consider a N×N square board where N≥3 is an odd integer. The caterpillar Carl sits at the center of the square; all other cells contain distinct positive integers. An integer n weights 1\slash n kilograms. Carl wants to leave the board but can eat at most 2 kilograms. Determine whether Carl can always find a way out when
a) N=2003.
b) N is an arbitrary odd integer. combinatoricssquareboardwayweightsgrid