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.
Revive the IMO marathon.
- 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.
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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