There was a problem I was introduced to in grade school which my teacher claimed that not even his graduate level students could solve, and it went a little like this. You have a set of boxes in a brick-like pattern which looks like so:
your challenge is to draw a single line which intersects all walls in the drawing exactly once, but not your line itself. You can start anywhere you like, except on a wall or corner. For example, here is an attempt I made at solving this puzzle:
The circled red walls are walls that still need to be crossed, but I cannot cross them without crossing a wall twice, or crossing my own line.
My question comes in not looking for a solution, but an answer. Does this puzzle have a solution, and how do we prove it?