> >You're given a crossword-puzzle-grid, a list of numbers grouped by the
> >number of digits in each one and then sorted in numerical order, and one
> >number placed in the grid. You then try to logically figure out where
> >each of the rest of the numbers fit in the grid.
> >
...
> >So, am I nuts? Or just really, really weird?
> >
> > Julia
Everybody likes different things. To me, those sound too
much like "work". I would just transfer it into Graph Theory and
write a program to solve the puzzles.
But they're way better than word search puzzles, in my
view. I have an algorithm for word search puzzles: Take the
first word. Find its first letter. Go through the grid looking
for the first letter. Now look around each instance for the
second letter of the word. Etc. I find anything that easy to
automate BORING.
I also have a book of "Mensa Math and Logic Puzzles". But
they are too hard to be interesting. If I ever need examples of
NP-complete recreational problems, I have a book of them...
>
> I like them too. Haven't done them in a long time, but they are better than
> normal crossword puzzles or a word search type.
>
> I'm assuming a program can be written, where you'd almost have to solve the
> whole thing before you can get the first one. Do you think these are now
> made by hand or with a 'puter?
>
> Kevin T. - VRWC
You mean, "Are there puzzles of this type where for any number
k much less than the total number of words n, and for any subset of
k word-spaces in the grid, that there are multiple valid ways to fill
in the k word-spaces."?
That sounds plausible. I don't have a good grip on the
problem, so I can't say for sure. If it were true, the existence
of such puzzles could probably be shown by a counting argument.
Ideally, a puzzle like this should appear to be NP-hard
(i.e. one would just have to try everything), but then on closer
inspection reveal a "back door" to deducing a solution step-by-step.
It might be possible to find these automatically, but I'd HOPE that
someone was checking by hand to be sure that solving them would
feel satisfying.
---David
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