#1




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. 
#2




Re: *ANSWER* Question 9 with triangles
Quote:
http://book.caltech.edu/bookforum/showthread.php?t=2606 and we can discuss this further.
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#3




Re: *ANSWER* Question 9 with triangles
Well, I see that an Ngon (won't say which) is easy to shatter, and the (N+2)gon is easy to see that it can't be shattered. So I know which of the answers to choose, but I'm still not clear on the (N+1)gon in between.

#4




Re: Question 9 with triangles
I took out the *ANSWER* warning since the discussion seems safe so far.
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Where everyone thinks alike, no one thinks very much 
#5




Re: Question 9 with triangles
Ah, well, I guess an (N+1)gon works too  brute force check on all triangles. Not very elegant, but it works.

#6




Re: Question 9 with triangles
I was having about the same troubles figuring out the perceptron problem, but I think looking in the book (*ANSWER*) helps a lot.

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