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New 2s pattern spotted today
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s
Posted - 2006.04.24 05:09:14
Quote:
Originally Posted by procrastinator
Quote:
Originally Posted by puzzlelover

Here's one instance of the above.

And here's the other:



Do you know what chairman means by "the Highlander argument"?
That was my next question!   I think I've read most of this forum, but I don't recall seeing the Highlander argument defined anywhere, and just saw it mentioned in this thread.

Is the Highlander argument just the ruling out of patterns by non-uniqueness?  Any interesting etymology there?

I've seen uniqueness deductions briefly mentioned in the forum, but never discussed in depth.  I gather non-uniqueness is what rules out this pattern.

The sudoku world has discussed uniqueness deductions extensively.  Relying on uniqueness deductions to solve puzzles like sudoku and slither link seems questionable aesthetically, especially since non-unique sudokus are fairly common in practice.  But it's a powerful pragmatic tool, even though it feels like cheating   I've used uniqueness deductions in slither link occasionally.

So this pattern is one of them.  Cool!  I think this is another, along the same line.  If all ?s are blank, then 4 x's can be deduced (no matter where the edges are).

procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.04.24 07:49:10
Quote:
Originally Posted by puzzlelover

Is the Highlander argument just the ruling out of patterns by non-uniqueness?  Any interesting etymology there?

The movie has a catchphrase "There can be only one".

Quote:
Originally Posted by puzzlelover

Relying on uniqueness deductions to solve puzzles like sudoku and slither link seems questionable aesthetically, especially since non-unique sudokus are fairly common in practice.

I don't like the sound of a non-unique logic puzzle? Seems like for a lot of deductions you'd have to trace four possibilities right to the end to know which two worked - and trust yourself to get it right. But are chains of implication shorter in sudoku?

Uniqueness is mandatory for slither link, but obviously you never _have_ to use it, so I chose not to when I was trying to make the few available puzzles last longer. After discovering Kwon-tom Loop, of course, aesthetics  has taken a back seat to raw speed - I even use Fix Position fairly regularly these days. And when I discovered there were simple patterns for uniqueness, I found them very elegant indeed.

Quote:
Originally Posted by puzzlelover

So this pattern is one of them.  Cool!  I think this is another, along the same line.

Actually, that was the first uniqueness pattern posted to the forum (by foilman, when asked whether solutions were unique) which lead to us all starting to notice more of them.
chairman
Kwon-Tom Obsessive
Puzzles: 1395
Best Total: 17m 32s
Posted - 2006.04.24 16:18:13
The diagonal 1-2-1 series can be found at the topic started by Dan, called 'couple of questions'. It was then posted by Drnull. Was it originally of Foilman? I read it  only after my first post, otherwise I would have referred to this pattern as well. The first time I used the uniqueness argument on slither links, I was a bit reluctant too. Not because of aesthetical reasons, but because if the puzzle does have more than one solution, the argument will ruin the search and you'll find no solution at all. (Criticizers on the two sequels of Highlander commented "there should have been only one" (and they were right). I don't think we will ever have to say that to Foilman.)
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