Consider a 6 by 6 square gameboard. Your piece is Y and the opponent's piece is X. The opponent's piece does not move. Your piece is allowed to move one square at a time diagonally left or right, unless the opponent's piece is on the way. In that case, your piece is allowed to jump over the opponent's piece to the square two rows away. How many different paths will lead you to the available positions (a, b, or c) in the top row? Fully explain your solution.

	a		b		c
	X
				Y