BrainDen.com - Brain Teasers

# witzar

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2. ## All the people like us are We, and everyone else is They.

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... "

4. ## Partitioning a Rectangle...

Look here for proofs (there are many): http://mathdl.maa.org/images/upload_library/22/Ford/Wagon601-617.pdf

7. ## Am I wrong?

0.999... = 1 0.333... = 1/3 1/3 + 1/3 + 1/3 = 1
8. 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.
9. 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.
10. 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.
11. 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.
12. There are others. Consider for example 11001100... (buttler says: 11001100...)
13. http://en.wikipedia.org/wiki/Derangement
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