Suppose we have empty chessboard, and king on A1
King can move either up (a1-a2) or right (a1-b1), how many possible routes can king take to arrive at h8?
My thoughts are to retrace kings moves backward - ie king can arrive on h8 from either h7 or g8, king can arrive on b1 only from one square - a1.
However, when I try simplify/visualise route, it doesnt quite work that way, let me elaborate.
Lets take 2x3 board:
There is distinctly 3 ways to arrive at
By either moving to right, up, up
up, right, up
or up, up, right
However when i count possibilities to arrive:
2*2=4, not 3.. What am I missing here?