NL-NWO 1995 Problem 1

A kangaroo jumps from lattice poin to lattice point in the coordinate plane. It can make only two kinds of jumps: $(A)$ $1$ to right and $3$ up, and $(B)$ $2$ to the left and $4$ down. $(a)$ The start position of the kangaroo is $(0,0)$ . Show that it can jump to the point $(19,95)$ and determine the number of jumps needed. $(b)$ Show that if the start position is $(1,0)$ , then it cannot reach $(19,95)$ . $(c)$ If the start position is $(0,0)$ , find all points $(m,n)$ with $m,n \ge 0$ which the kangaroo can reach.