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.

(In reply to re(2): Sparseness .....spoiler by ed bottemiller)

It was not obvious that you refer to the "sparsest set ".

No doubt, you fully ubnderstood the problem, but Justins explanation sounds much more rigid.

 Anyway , we all know that we don't have to list all the possible partitions of 9 into 4 or less integers.

Posted by Ady TZIDON on 2010-09-15 18:27:40