Problem 1:
There are $2011$ mathematicians in a party. It is known that, Mahbub, the host of the party (who is also a mathematician) knows all other mathematicians. Two mutually unacquainted mathematicians will become friend of each other eventually after the party if they have a common friend/acquaintance (who will introduce them to each other of course). After the end of the party how many pairs of mathematicians will be left who are not yet introduced to each other?
BdMO National Secondary 2011/1
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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learn how to write equations, and don't forget to read Forum Guide and Rules.
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FahimFerdous
- Posts:176
- Joined:Thu Dec 09, 2010 12:50 am
- Location:Mymensingh, Bangladesh
Re: BdMO National Secondary 2011/1
As Mahbub is everyone's friend, there is no pair which doesn't have a mutual friend. So, the answer is 0.
Your hot head might dominate your good heart!
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Ayesha Siddiqua
- Posts:1
- Joined:Sun May 01, 2011 1:09 pm
Re: BdMO National Secondary 2011/1
is the ans is enough??i know that the ans is 0.bt i think we have to prove it though i don't knw the way to prove.
Re: BdMO National Secondary 2011/1
Such problems don't need rigorous proofs. Just you have write down what made the sense in you.
One one thing is neutral in the universe, that is $0$.