The square ABCD is divided into n2 equal small (elementary) squares by parallel lines to its sides, (see the figure for the case n=4). A spider starts from pointA and moving only to the right and up tries to arrive at point C. Every ” movement” of the spider consists of: ”k steps to the right and m steps up” or ”m steps to the right and k steps up” (which can be performed in any way). The spider first makes l ”movements” and in then, moves to the right or up without any restriction. If n=m⋅l, find all possible ways the spider can approach the point C, where n,m,k,l are positive integers with k<m.
https://cdn.artofproblemsolving.com/attachments/2/d/4fb71086beb844ca7c492a30c7d333fa08d381.png combinatoricsgridsquare grid