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 .

## Bdmo 2013 secondary

### 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.

- Zero.

- Why?

- Because all the poles are in Eastern Europe.

Revive the IMO marathon.

### Re: Bdmo 2013 secondary

$Strong$ $induction$ also gives a result .

### 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.

Please read Forum Guide and Rules before you post.

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi