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not a pattern
chairman
Kwon-Tom Obsessive
Puzzles: 1395
Best Total: 17m 32s
Posted - 2006.04.26 22:32:56


I'm still intrigued by the uniqueness argument, or highlander argument, or lone 2's argument, what's in a name.

The fragment above is not a pattern as it is not likely to ever occur in a daily puzzle, but I like it as a little local puzzle itself. There are no borders involved. Can you find seven new lines and eight new x-es?
drnull
Kwon-Tom Obsessive
Puzzles: 901
Best Total: 23m 25s
Posted - 2006.04.27 13:18:53
I was able to add 2 lines and an x relatively easily.  (ok, it's not trivial, but compared to the disproving of the rest of your proposed solution it was easy...)

After I added in those lines, I just started trying different lines, and seeing which sets of lines led to ambiguity.  I got it with the following:


If you put a line in one of those ?'s, you get one form, if you choose the other, you get another form.  Both forms have the same "endpoints", if you will.  However, the forms have different internal geometry.  This matters, depending on what the rest of the puzzle looks like.

However, for what it's worth, I like the usage of the highlander argument here.  It does gain you 2 lines and an x.
chairman
Kwon-Tom Obsessive
Puzzles: 1395
Best Total: 17m 32s
Posted - 2006.04.27 14:21:08
Let's make it a little more transparent. If you choose one of your question marks to be a line, and the other one a cross, you'll get the form



the other way round results in



Suppose one of these is part of the global solution. Then you can replace it by the other one and get another global solution.
So the forms rule each other out. Isn't this the same way of reasoning that led to the two lines you found?
drnull
Kwon-Tom Obsessive
Puzzles: 901
Best Total: 23m 25s
Posted - 2006.04.27 14:28:05
Ahh, there we go.  I was thinking that only one of those would be valid depending on the configuration of the rest of the puzzle.  But what I was doing was connecting two halves and creating two loops in one puzzle, and assuming that it would create a valid solution in the other puzzle.  That's not the case, though.  If those two ends are connected in both puzzles, then both puzzles are invalid, so that's can't be true.

Ok, my bad.    Nice "non-pattern", btw.  That was fun.

Oh, and the 8th x took me a few seconds of staring at my 7-line, 7-x solution.  Duh, closed local loop. 
Last edited by drnull - 2006.04.27 14:30:00

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