SELF-REFERENTIAL APTITUDE TEST

[Kire]

SELF-REFERENTIAL APTITUDE TEST, by Jim Propp

The solution to the following puzzle is unique; in some cases the
knowledge that the solution is unique may actually give you a short-cut
to finding the answer to a particular question, but it's possible to
find the unique solution even without making use of the fact that the
solution is unique. (Thanks to Andy Latto for bringing this subtlety
to my attention.)

I should mention that if you don't agree with me about the answer to #20,
you will get a different solution to the puzzle than the one I had in mind.
But I should also mention that if you don't agree with me about the answer
to #20, you are just plain wrong. :-)

You may now begin work.

More: http://www.math.wisc.edu/%7Epropp/srat-Q