Question 64
We are given a sheet of paper in the form of a rectangle $x \times y$, where $x$ and $y$ are integer numbers larger than $1$. Let us draw a lattice of $x \times y$ unit squares on the sheet. Rolling up the rectangle and gluing it along its opposite sides we shape a lateral surface of a circular cylinder. Join each two distinct vertices of the marked unit squares on the surface by a segment. How many of all these segments are passing through an interior point of the cylinder? In the case $x \gt y$ decide when this number of "internal" segments is larger — for the cylinder with bases of perimeter $x$, or $y$? (Vojtech Bálint)
