One of my colleagues sent me the equivalent question, the only difference being the word "bus" instead of "coach" for the vehicle. As the Problem Section Editor of MathAMATYC Educator, I knew of the first two versions, but not the one with infinitely many buses. So, I am using it in an upcoming issue.

Of course, I was not aware that this was online until I talked about it with somebody else, who then sent the link. And that is how I came to be here.

I spent under an hour on solving the "infinite number of buses each with infinitely many people" problem directly. I am not sure how many of my readers (mostly community college math instructors) would care, but my dedication is first to them, not here. Yes, I would love to give it here, as I believe that it is much simpler than what is posted here.

Unfortunately, there seems to be some ethical sense that I would probably have to drop the question from my future column, so I will compromise. If anybody writes me, I will send a short Word 2003 document with solution.