Question 24
C1 (FIN) IMO1 We are given a positive integer $r$ and a rectangular board $ABCD$ with dimensions $|AB|=20$, $|BC|=12$. The rectangle is divided into a grid of $20\times12$ unit squares. The following moves are permitted on the board: One can move from one square to another only if the distance between the centers of the two squares is $\sqrt r$. The task is to find a sequence of moves leading from the square corresponding to vertex $A$ to the square corresponding to vertex $B$.
(a) Show that the task cannot be done if $r$ is divisible by $2$ or $3$.
(b) Prove that the task is possible when $r=73$.
(c) Is there a solution when $r=97$?
(a) Show that the task cannot be done if $r$ is divisible by $2$ or $3$.
(b) Prove that the task is possible when $r=73$.
(c) Is there a solution when $r=97$?