Induction or pigeonhole principle or what? Hello I've this exercise but I am not sure how you prove it formally. 
Some guy $G$ was writing book for $81$ hours in $10$ consecutive days. Show that there was $2$ consecutive days that included guy $G$ writing book for at least $17$ hours combined(from 2 days).
I think this example sucks because he could be writing for $8,1$ hours each day and what then? This should be precised that he had only written in full hours. Ok - I get it now(I get it at intuitive level), but how to show this the math way?.
Should I use induction, pigeonhole principle or what? Also could you tell me what is classic example of this type of exercise, so I can learn more. You see If I only knew how this problem is called I wouldn't have to write this question.

Hint: If it wasn't the case, what is the most time he could write on the first two days? The next two days? etc.
Technically, I suppose, you could use the pigeonhole principal.
And yes, you have to assume that he is counting integer hours, not fractional. Otherwise he could write $8.1$ hours per day.
