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daily puzzle (Sunday, 11th June 2006)
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s
Posted - 2006.06.11 23:43:01
This puzzle was pretty tough for me.  I used a couple of Highlander deductions in corners -- felt like cheating, but I needed every lead I could get.  I managed 48 minutes and felt pretty good (for me).

Even on a third solve, remembering key points from the first two solves, I couldn't beat 17 minutes.  How on earth do you wizards solve these quickly the first time?
Last edited by PuzzleLover - 2006.06.12 02:31:21
astrokath
Kwon-Tom Obsessive
Puzzles: 3093
Best Total: 13m 42s
Posted - 2006.06.12 07:15:32
As far as highlander goes, I got most use out of it on that puzzle for loops around twos - as far as I remember, there were a few places where I had, oh, something like this:

...and the lack of other numbers around the 2 meant that I knew I HAD to have this situation: in order to avoid something like this:

Pure logic didn't take me as far as it did on saturday though, so a fair bit was ruling out false routes via trial and error.  Finding the most productive areas to start looking is a learned skill in my case - these types of puzzles used to take me a LOT longer when I hadn't done many of them, back in the days when it was only Foilman who could break the 1hr mark for the weekly total.
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s
Posted - 2006.06.12 08:15:41
Yeah, there were a couple of those in the lower corners.  I added it to my recognized pattern repertoire, and it helped on Monday too

Another interesting pattern in the upper right corner (corner shown) that I didn't recognize for awhile:


The ? on top must be x, since otherwise the 2 on the right can't be completed.  But I didn't see this until very late in the first solve.
astrokath
Kwon-Tom Obsessive
Puzzles: 3093
Best Total: 13m 42s
Posted - 2006.06.12 09:16:35
Yeah, that was another useful one that I didn't spot at first glance.
mathmaniac
Kwon-Tom Obsessive
Puzzles: 1198
Best Total: 20m 57s
Posted - 2006.06.12 12:38:25
I always heard you talking about the highlander argument and I couldn't figure out what is was and it turns out that I've used it all the time!
Acorn
Kwon-Tom Obsessive
Puzzles: 555
Best Total: 42m 58s
Posted - 2006.06.14 20:24:20
I don't understand your example with the twos?  Why can't it be like this?

or even like this?

I must be missing something important because I dont' understand at all.  I guess that explains why my time hasn't improved much.

Even on the beast I can do quite a lot of it logically but I still have to use pencil to try some spots so I can get further.
matth314
Kwon-Tom Obsessive
Puzzles: 2431
Best Total: 16m 52s
Posted - 2006.06.14 20:47:40
The idea is that if you have the situation which astrokath says you want to avoid--

then it can go either way. It doesn't matter which way it goes, and therefore it has two solutions. We know that this is not possible because every puzzle has only one solution. So you must have the two lines cornering the two and forcing it to go one particular way:
foilman
Kwon-Tom Admin
Puzzles: 1718
Best Total: 24m 8s
Posted - 2006.06.14 20:59:52
Yes, that's right - you can take advantage of the fact that you know the puzzle has one unique solution, so if something can give you two solutions, it must be wrong. In fact, if you try the alternative and see how it plays out, eventually it will result in an unsolvable puzzle. The highlander argument is just a shortcut pattern to save time looking ahead.
Acorn
Kwon-Tom Obsessive
Puzzles: 555
Best Total: 42m 58s
Posted - 2006.06.14 21:09:02
Normally I would assume that when I do more of the puzzle I will be forced to make a choice as to which way this corner works.

Am I wrong?  Or do you only use this theory when you have a very small space left to fill in?

That would certainly explain why I end up with some large gaps in my puzzles sometimes.
mathmaniac
Kwon-Tom Obsessive
Puzzles: 1198
Best Total: 20m 57s
Posted - 2006.06.14 21:36:32
It only works when you don't have any numbers around the 2.
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s
Posted - 2006.06.14 22:36:51
Quote:
Originally Posted by acorn
Normally I would assume that when I do more of the puzzle I will be forced to make a choice as to which way this corner works.

Am I wrong?  Or do you only use this theory when you have a very small space left to fill in?

That would certainly explain why I end up with some large gaps in my puzzles sometimes.
This is true in theory.

In practice, it could be very difficult to solve some puzzles without using this argument.  It might involve several remote choices with complicated interactions.

I'm confident foilman's puzzle generator includes this form of the Highlander argument when it rates puzzle difficulty.  So it has no idea how difficult the puzzle could be without using this pattern, and it could be VERY difficult.

I'd say the significance of using this Highlander pattern is the opposite of  what you said.  If you only have a small area to fill in, you can solve without Highlander so it doesn't matter.  It's when there are large areas and you haven't yet found (by other deductions) the context around the 2 that it makes a big difference.
foilman
Kwon-Tom Admin
Puzzles: 1718
Best Total: 24m 8s
Posted - 2006.06.15 08:22:16
Quote:
Originally Posted by puzzlelover
I'm confident foilman's puzzle generator includes this form of the Highlander argument when it rates puzzle difficulty.  So it has no idea how difficult the puzzle could be without using this pattern, and it could be VERY difficult.
Actually it doesn't... the difficulty is calculated during puzzle generation, and at that point it can't use highlander arguments because it's not guaranteed there's only one solution!

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