Difference between revisions of "1978 IMO Problems/Problem 6"
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Revision as of 21:17, 5 August 2017
An international society has its members from six different countries. The list of members has 1978 names, numbered ![$\color[rgb]{0.35,0.35,0.35}1, 2, \ldots, 1978$](http://latex.artofproblemsolving.com/3/f/0/3f0e6a79359951ea282570f257e40f1e373d4277.png)
. Prove that there is at least one member whose number is the sum of the numbers of two (not necessarily distinct) members from his own country.
Lets consider the members numbered 
. If these members belong to 
countries then, by the Pigeonhole principle, there must exist a country to which a minimum of 
