Pigeon Hole Principle - 14 days, 10 physical exercises. How will you do PE on consecutive days at least once in the next fortnight.?

Question

I was given this question. Maths is a weakness of mine and I'm really struggling to understand what this question is asking, and how to solve it. My notes indicate it's a pigeon hole principle but I'm unsure.

"You prepare a schedule of your physical exercises for the next fortnight (14 days). You don’t do physical exercise more than once a day. If you have 10 PE sessions planned, explain using the counting principles covered in class how this means you will do PE on consecutive days at least once in the next fortnight."

Thanks in advance :)

Answer 1

Let $\ n\ $ be the number of PE lessons scheduled for days immediately followed by a day free of any PE lesson. These lessons plus the following lesson-free day must occupy a total of $\ 2n\ $ days, at most one of which (if it is the day following the last lesson) can lie outside the allowed $14$-day period. This leaves at most $\ 15-2n\ $ days available to be occupied by the remaining $\ 10-n\ $ lessons. Thus, $\ 10-n\le15-2n\ $, giving $\ n\le5\ $. Thus, there must be at least $\ 5\ $ lessons on days that are immediately followed by a day with another lesson.