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≥0 which the kangaroo can reach. analytic geometrycombinatorics unsolvedcombinatorics