> -----Original Message-----
> From: Steve Wampler [mailto:[EMAIL PROTECTED] 
> Sent: Thursday, April 12, 2007 7:54 AM
> To: Group, Unicon
> Subject: Re: [Unicon-group] Making the puzzle more interesting...
> 
> 
> I attached a solution to the general case.  
...
> I can't call it "my"
> solution because I've borrowed some ideas from code Steve 
> Hunter sent me (the most notable being the use of set 
> intersection to reject invalid pair couples like:  X:Y & Y:Z  
> (same state name used twice) - I had been using a more 
> brute-force check.

I wonder what the optimal algorithm is?  Right now, everyone's guessing
and testing code.  That's fine, but we don't yet know what's possible
(in the k^n vs. n^2 vs. n log n sense).  

For that matter, what is a correct statement of the "general" case,
going beyond the simple puzzle about 50 state names?  It would be an
interesting subject for theoretical analysis.

Looking back a bit, no one seems to have followed up on an interesting
suggestion someone made about using prime numbers to solve the puzzle.
(Unfortunately, I have lost the original posting so I cannot credit the
poster.)  I think the suggestion was to assign prime numbers to the
letters of the alphabet and then do a product of the letter-values of
the state names.  I haven't tested this idea.  Has anyone else?  Does it
generate unusably huge numbers?  I'll try to do some experiments in this
area ... maybe ... time permitting.

> I hope people have (are still having) fun with this!

This has been great fun, though right now I'm just reading and
pondering.  Jeez Louise, who's got time to write code?!?

Charlie Hethcoat

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