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Old 04-18-2013, 01:41 PM
Michael Reach Michael Reach is offline
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Join Date: Apr 2013
Location: Baltimore, Maryland, USA
Posts: 71
Default Question 9 with triangles

I am having a hard time finding a good way to visualize this. Maybe someone can make suggestions.

One thing I decided early on: A "best" set of N points (with a maximal number of dichotomies) has to be convex. If it is concave, make the point on the inside -1 and three points surrounding it +1 and it won't work.

Once the set is convex (maybe you can put them on a circle WLOG or some such), I _think_ I can guess the number that will force no breaking, but I don't have a clear argument.
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