0

Let $$S \subset N_{100}= \{1,2,3,4, \dots, 100 \}$$ with $|S|=51$. Then prove for any such $S$ it is possible to select two numbers from $S$ such that one is a multiple of other.

I wasn't able to proceed. How should I start. I think it needs Pigeon Hole Principle.

Jyrki Lahtonen
  • 140,891
user567182
  • 227
  • I added the final $100$ in the list of elements of $N_{100}$. This is absolutely necessary for the question to make sense. Note that the notation $N_{100}$ is not standard, so a precise description must be given. Leaving those three dots/ellipsis at the end of the list conveys the intent that the list will continue indefinitely. – Jyrki Lahtonen Jun 22 '18 at 07:13
  • For the record, I also support closing this question for lack of context. Saying that you "don't know how to start" is not sufficient context. You were given related example problems with absolute certainty. – Jyrki Lahtonen Jun 22 '18 at 07:15
  • 1
    Yeah, ,that other question answers this perfectly. – fleablood Jun 22 '18 at 07:27

0 Answers0