MathDB

In a

19\times 19

board, a piece called dragon moves as follows: It travels by four squares (either horizontally or vertically) and then it moves one square more in a direction perpendicular to its previous direction. It is known that, moving so, a dragon can reach every square of the board. The draconian distance between two squares is defined as the least number of moves a dragon needs to move from one square to the other. Let

C

be a corner square, and

V

the square neighbor of

C

that has only a point in common with

C

. Show that there exists a square

X

of the board, such that the draconian distance between

C

and

X

is greater than the draconian distance between

C

and

V

Problem Statement