2007 OIM Problems/Problem 4
Problem
On a 
grid board, a piece called a "dragon" jumps from side to side in the following way: it moves 4 squares in a direction parallel to one of the sides of the board and
1 square in a direction perpendicular to the previous one. It is known that, with this type of jumps, the dragon can move from any square to any other. The dragonian distance between two squares is the fewest number of jumps the dragon must take to move from one square to another.
Let 
be a square located in a corner of the board and let 
be the square next to that touches a single point. Prove that there is some square 
on the board such that the dragonian distance from to is greater than the dragonian distance from to .
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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