# Functions Problem 8

### Solution

Divide the sheet of agar into 361 squares with side length 1.
We'll consider that each square includes the boundary of the
square as well as its interior, so the squares overlap slightly.

We need to choose 380 points in the larger square as locations for
mold samples. By the Pigeonhole principle, with 380 choices to make over
19*19=361 regions, at least two of the samples must be in the
same square region.

Recall the Distance Formula for 2D points. If two points are part of
the same square region of area 1, the maximum distance between them is
\(\sqrt{2}\). Because we have said that there are at least two points
that are part of the same square region, two of the mold samples
must have been placed too close together. So the sheet of agar
wasn't large enough.