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 20110323 17:03:55 