It's not at all impossible. Points can be on the line. If M and N are both odd, the line will go through at least one red and at least one blue point.

Of course, that still wouldn't address the problem with infinite sets.

In fact, it does work with infinite sets, and it works in more dimensions as well. This theorem, saying that in d dimensions, given d sets there is a hyperplane of dimension d - 1 that divides all sets in two parts of equal size, is also known as the "ham-cheese sandwich cut", because the theorem implies that you can always divide a ham-cheese sandwich in two equal parts (both parts having the same amount of ham, cheese and bread) with a single cut, even if you leave the cheese in the fridge.

Abigail

In reply to Re: Suggestions for writing a Perl application by Abigail-II
in thread Suggestions for writing a Perl application by phax

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