Question 66
Let $r$ be a positive integer. The following game is being played on a rectangular board divided into $20 \times 12$ unit squares. One is allowed to move a piece from a square to another, if the distance between (the centres of) these squares is $\sqrt{r}$. The goal is to find a sequence of moves leading from the bottom left corner to the bottom right corner.
a) Show that the goal is impossible to fulfill if $r$ is divisible by 2 or 3.
b) Prove that the task is possible when $r = 73$.
c) Is there any solution when $r = 97$?
a) Show that the goal is impossible to fulfill if $r$ is divisible by 2 or 3.
b) Prove that the task is possible when $r = 73$.
c) Is there any solution when $r = 97$?