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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