Bdmo 2013 secondary

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Tahmid
Posts: 110
Joined: Wed Mar 20, 2013 10:50 pm

Bdmo 2013 secondary

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
Posts: 136
Joined: Thu Aug 29, 2013 11:21 pm
Location: Varies.

Re: Bdmo 2013 secondary

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
Posts: 110
Joined: Wed Mar 20, 2013 10:50 pm

Re: Bdmo 2013 secondary

\$Strong\$ \$induction\$ also gives a result .

*Mahi*
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Re: Bdmo 2013 secondary

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.