MathDB

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.

Problem Statement