There's a problem in my textbook that I'm having difficulties understanding. The solution given skips steps and is hard to decipher. The problem is as follows:
"During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days during which the team must play exactly 14 games."
I don't know how to arrive at the conclusion of 14 games. Anyone who can help me understand this application of the pigeon-hole principle would be greatly appreciated, thank you.