Proves that

  • Thread starter al-mahed
  • Start date
  • #1
261
0
Given a positive whole number n, [tex]\exists[/tex] N with the following property: if A is a subgroup of {1,2,...,N} with at least N/2 elements, then there is a positive whole number m<= N - n such that

|A [tex]\cap[/tex]{m+1, m+2,..., m+k}|>=k/2

[tex]\forall[/tex] k = 1, 2, …, n.
 
Last edited:

Answers and Replies

  • #2
CRGreathouse
Science Advisor
Homework Helper
2,820
0
Just look at the top half and the bottom half.
 
  • #3
261
0
Hi, I'll be glad if you put your solution here. I already saw a proof, but I don't know if it's correct.
 
  • #4
261
0
this is an olympic problem, by the way
 

Related Threads on Proves that

Replies
25
Views
2K
  • Last Post
Replies
7
Views
10K
  • Last Post
Replies
8
Views
944
  • Last Post
Replies
5
Views
2K
Replies
3
Views
1K
Replies
1
Views
2K
Replies
11
Views
3K
  • Last Post
Replies
2
Views
2K
Replies
4
Views
23K
Replies
26
Views
2K
Top