Consider the grid of points X= (m, n) 0 m, n 4 . We say a pair of points (a, b),(c, d) in X is a knightmove pair if (c=a 2 and d=b 1) or (c=a 1 and d=b 2) . The number of knight-move pairs in X is:

Step-by-step solution

Consider the grid as shown. Each line represents the allowed move from one and point of line to other end point of line we can see the movement allowed in 3 2,2 2 rectangle, vertical or horizontal. In each rectangle there are 4 moves allowed and total number of rectangle are 12 . Total allowed moved =12 4=48 .