witzar
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Everything posted by witzar
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All the people like us are We, and everyone else is They.
witzar replied to bonanova's question in New Logic/Math Puzzles
1. The difference of two real numbers numbers always exists and is also a real number. 2. A real number cannot be "infinitesimally small". 3. Please don't answer "thanks for the explanation, but I'll stick to... " -
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Look here for proofs (there are many): http://mathdl.maa.org/images/upload_library/22/Ford/Wagon601-617.pdf
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Polygons of infinite perimeter but finite area
witzar replied to bonanova's question in New Logic/Math Puzzles
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0.999... = 1 0.333... = 1/3 1/3 + 1/3 + 1/3 = 1
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I should have used term "reflection" instead of "symmetry". Sorry for that. For me cases are equivalent when there is an isometry of a cube that transforms one case into another. For you cases are equivalent when there is an orientation preserving (or rotational, which is the same) isometry of a cube that transforms one case into another.
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Thanks. Now I see why I get 20 and you get 22. You treat two cases as equivalent if there exists rotation that transforms one case into another. And I allow symmetries as well. For example (1,6) and (1,8) are equivalent for me but not equivalent for you.
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Can you improve your program to print solutions as well? I've found 20 and was pretty sure there are no more. So now I'm curious.
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There are 4 edge-edge cases: 1) parallel sharing face 2) parallel not sharing face 3) sharing edge 4) not parallel and not sharing edge I think you missed it.
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There are others. Consider for example 11001100... (buttler says: 11001100...)
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http://en.wikipedia.org/wiki/Derangement
