For each point in the plane a real number is assigned such that for every triangle its incenter is assigned the mean of the numbers assigned to its vertices.

Prove that the same number is assigned to every point in the plane.

(In reply to re: Solution. Hope this makes sense. by Bractals)

Probably not.

What, you didn't like how I reduced the problem to a simpler one?

I would think a solution would rely on showing that a few points must be equal and then expanding this.  A ring of 6 equilateral triangles around a central point might help.

Posted by Jer on 2011-03-23 17:03:55