IMO Shortlist 1966 problem 24
Dodao/la:
arhiva2. travnja 2012. There are
![n\geq 2](/media/m/e/d/b/edbb3c15913fef4235c90cca2333a608.png)
people at a meeting. Show that there exist two people at the meeting who have the same number of friends among the persons at the meeting. (It is assumed that if
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
is a friend of
![B,](/media/m/1/6/e/16e519ccc501d3fbc4fe4ab09a16195c.png)
then
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
is a friend of
![A;](/media/m/4/d/a/4daf691252acf300098c3276997f620f.png)
moreover, nobody is his own friend.)
%V0
There are $n\geq 2$ people at a meeting. Show that there exist two people at the meeting who have the same number of friends among the persons at the meeting. (It is assumed that if $A$ is a friend of $B,$ then $B$ is a friend of $A;$ moreover, nobody is his own friend.)
Izvor: Međunarodna matematička olimpijada, shortlist 1966