Question

solve this if you want brainleist

Answer 1

Assume, wlog, the knight moves q steps to the right after its p steps. Let the valid moves for the knight be "LU", "UR", "DL", "RD" i.e. when it moves Left, it has to go Up("LU"), or when it goes Up , it has to go Right("UR") and so on.

Let the knight be stationed at (0,0). We note that after any move its coordinates will be integer multiples of p,q. Let its final position be (pk,qr) for k,r∈Z. We follow sign conventions of coordinate system.

Let knight move by −pk horizontally and −qk vertically by repeated application of one step. So, its new position is (0,q(r−k)) I am thinking that somehow I need to cancel that q(r−k) to achieve (0,0), but don't be able to do the same.