Bdmo 2013 secondary

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Tahmid
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Bdmo 2013 secondary

Unread post by Tahmid » Mon Mar 02, 2015 7:29 pm

There are $n$ cities in a country. Between any two cities there is at most one road. Suppose that the total
number of roads is $n$ . Prove that there is a city such that starting from there it is possible to come back to it
without ever travelling the same road twice .

Nirjhor
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Re: Bdmo 2013 secondary

Unread post by Nirjhor » Mon Mar 02, 2015 9:10 pm

A graph with $n$ vertices and $n$ edges contains a cycle. (With $n-1$ edges and no cycles it must be a tree, so the $n$th edge forms a cycle.)
- What is the value of the contour integral around Western Europe?

- Zero.

- Why?

- Because all the poles are in Eastern Europe.


Revive the IMO marathon.

Tahmid
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Joined: Wed Mar 20, 2013 10:50 pm

Re: Bdmo 2013 secondary

Unread post by Tahmid » Mon Mar 02, 2015 9:53 pm

$Strong$ $induction$ also gives a result . ;)

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*Mahi*
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Re: Bdmo 2013 secondary

Unread post by *Mahi* » Tue Mar 03, 2015 12:36 am

Previously posted here http://www.matholympiad.org.bd/forum/vi ... =13&t=2928 , also pinned at the top of forum home page. Please, for common problems, search the forum at least once. Topic locked.
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