(Solved): In chess, a Knight (the one that looks like a horse) moves in an L-shaped pattern as shown in the ...

In chess, a Knight (the one that looks like a horse) moves in an L-shaped pattern as shown in the left-hand diagram. The black Knight in the middle of the board could move to one of 8 squares, the white Knight in the corner can reach only one of two possible squares, leading to the old chess adage: A Knight on the rim is grim. a b c d e f g h a b c d e f g h a b c d e f g h 8 8 8 X X 7 7 7 6 6 5 5 4 3 3 3 15:0 2 2 1 1 5 a b c d e f g h a b c d e f g h a b c d e f g h Knights move like an L (a) (b) 1. Assume the white Knight starts on square bl as shown in figure (a). How many paths can the Knight take to reach the b8 square marked ”X”? Assume that the knight must make forward progress towards the 8th row with each move - it can never move backwards. One such path is shown. Hint: This problem involves the repeated application of the sum rule. 2. How many paths can the Knight take to reach X assuming that the Knight can never land on any of the 4 center squares marked in diagram (b). Again, only forward moves are allowed. 6 5 3 2 1 2 1 8 7 6 5 8 7 6 5 4 3 2 1 8 7 6 10 5 4 3 2 1