Question 10
On a $19 \times 19$ square grid board, a piece called a *dragon* jumps as follows: it moves $4$ cells in a direction parallel to one of the sides of the board and $1$ cell in the direction perpendicular to the previous one.
From $D$, the dragon can jump to one of the four positions $X$.
It is known that, with this kind of jump, the dragon can move from any cell to any other.
The dragonian distance between two cells is the smallest number of jumps the dragon must make to move from one cell to the other.
Let $C$ be a cell located in a corner of the board and let $V$ be the cell neighbouring $C$ that touches it at a single point.
Prove that there exists some cell $X$ of the board such that the dragonian distance from $C$ to $X$ is greater than the dragonian distance from $C$ to $V$.
From $D$, the dragon can jump to one of the four positions $X$.
It is known that, with this kind of jump, the dragon can move from any cell to any other.
The dragonian distance between two cells is the smallest number of jumps the dragon must make to move from one cell to the other.
Let $C$ be a cell located in a corner of the board and let $V$ be the cell neighbouring $C$ that touches it at a single point.
Prove that there exists some cell $X$ of the board such that the dragonian distance from $C$ to $X$ is greater than the dragonian distance from $C$ to $V$.