### Twenty Questions: some background

I occasionally read the newsgroup rec.puzzles, and on one such
occasion I ran across a puzzle called the
Self-referential
aptitude test, by Jim Propp.
It had a bunch of intertwined multiple-choice
questions such as, "The number of questions with the answer A is...",
or "The answer to this question is the same as the answer to
question...".
The S.R.A.T. was an amusing puzzle, and I had fun solving it, but
I was left thinking, if *I* were going to construct a puzzle
like that, it would have *this* feature... So I constructed
my puzzle, which I call "Twenty Questions". The last question
illustrates the feature I had in mind:

20. The maximum score that can be achieved on this test is:
(A) 18
(B) 19
(C) 20
(D) indeterminate
(E) achievable only by getting this question wrong

I managed to find a friend willing to struggle through it in order
to prove it could be solved by a method other than exhaustive search
of all possible answers. (Thanks, Jim!) I also wrote a computer
program to doublecheck that my solution was correct, and that there
were no other possible solutions.
I posted the puzzle on
rec.puzzles, but got absolutely no response from the readers there,
just as I got no response other than dismay from the other friends I
showed it to.
So for a long time I had trouble finding an audience for this puzzle.
Then one day another friend (thanks, Pavel!) was headed for a gathering of puzzle
enthusiasts, and though the gathering was primarily focused on
physically manipulated puzzles, I gave him a copy of Twenty Questions
to share as he saw fit. One of the people who saw it there was
Ed Pegg, who runs the excellent site
mathpuzzle.com.
He wrote to me about it, and with my permission published the
puzzle on his site.

The mathpuzzle readership was definitely the right audience
for me! Over time, I saw various proposed solutions. At first,
they tended to be in error (e.g., in one case because the solver
was working from a faulty French translation),
but over time I saw at least two solutions that appeared correct,
yet different from the one I had in mind.
I went back to the program I'd written to "prove" that the
solution was unique, and using the two alternative solutions
managed to find the bug in the program. (How embarrassing!)

It turned out there were on the order of 50 solutions, which
was far too many. So
with a bit of additional effort, I came up with a
corrected version that I thought
re-established the uniqueness of the solution. Alas, someone
"cooked" this one also. I've taken a few additional swings
at finding a version that includes certain features while not
allowing any alternate solutions, but so far haven't found one
I'm willing to make any assertions about. :-(