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December 30th, 2010, 11:46 PM  #1 
Newbie Joined: Aug 2010 Posts: 23 Thanks: 0  colored hexagon =)
The points of the surface delimited by a regular hexagon of length side 1 are colored in 6 colors. Prove that there are two points of the same color situated at distance at least 1 .... How can we prove in this kind of q?u 
January 1st, 2011, 04:15 PM  #2 
Senior Member Joined: Nov 2010 Posts: 502 Thanks: 0  Re: colored hexagon =)
I would recommend starting at one corner, and call it color A. Did you know that a regular hexagon can be decomposed into 6 equilateral triangles? 

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