1996 IMO Problems/Problem 1

Problem

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 $20 \times 12$ 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 with $A$ as a vertex to the square with $B$ as a vertex.

(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) Can the task be done when $r=97$ ?

Solution

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1996 IMO (Problems) • Resources
Preceded by First Problem	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 2
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1996 IMO Problems/Problem 1

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