If 9 people are seated in a row of 12 chairs, then at least one consecutive set of 3 chairs is occupied by people.
Prove it.
There are a total of
12 chairs, and only
9 people. That leaves us
3 empty seats. That means that we can have, at most,
4 groups being seated.
There are 9 people amongst 4 groups, and 9 / 4 = 2.25, which is the average group size in this configuration.
Since our average is greater than 2, that is, 2.25 > 2, at least one set of occupied chairs will have 3 or more people seated in a row.

Posted by Justin
on 20100914 13:28:23 