29 Sep 2013

APMO 1989 Q4: Combinatorics: Upper Secondary Mathematics Competition Question


Let S be a set consisting of m pairs (a, b) of positive integers with the property that 1 ≤ a < b ≤ n. Show that there are at least



triples (a, b, c) such that (a, b), (a, c), and (b, c) belong to S.


[APMO 1989 Q 4]


Feel free to comment, ask questions and even check your answer in the comments box below powered by  Disqus Google+.

}

This space is here to avoid seeing the answers before trying the problem!

}

If you enjoy using this website then please consider making a donation - every little helps :-)

You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.

Don’t forget to follow Gifted Mathematics on Google+Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.
Related Posts Plugin for WordPress, Blogger...