Problem #178

In the coordinate plane, starting at (0,0), a kangaroo can either jump 1 unit to the right and 3 units up or 2 units to the left and 4 units down.

• Show that the kangaroo can reach the point (23,75) and determine the number of jumps required.

• Show that the kangaroo cannot reach the point (27,90) or the point (25,61).

• Characterize which lattice points (m,n) the kangaroo can reach.

Source: Dutch Mathematical Olympiad

The solution will be posted shortly.

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