help. How to SEE x wings or chains in the first place

Advanced methods and approaches for solving Sudoku puzzles

help. How to SEE x wings or chains in the first place

Postby kleinman » Sun Aug 21, 2005 1:10 pm

I have read about x wings and xy chains and swordfishes.
They all only seem to work when one has a number of cells with only 2 possible digits in them BUT how do you recognise the wing or chain or swordfish amongst all the other cells. Should you be trying to find all pairs including 1 particular number or what?
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Postby Jeff » Sun Aug 21, 2005 3:36 pm

Try here for x-wing and swordfish.
Try here for xy-chain.
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Postby Karyobin » Sun Aug 21, 2005 3:41 pm

Righty-ho, a few points drawn from my own experience:

1. I have never found, nor needed to use, a swordfish.

2. Ditto chains, though others here will disagree.

3. X-wings - yup, good stuff, these. It's nothing to do with the amount of digits in the cell, only the amount of times these possibilities appear in a row.

E.g. Let's say that in row 3, you can only have a '7' in cells 2 and 8. The same for row 9, again you can only have a '7' in cells 2 and 8. This means that, as a result of lots of clever stuff like conjugate pairing and the like, there can't actually be a '7' in any of the cells in columns 2 and 8, other than in the rows already mentioned. A couple of good descriptions can be found at:

http://www.angusj.com/sudoku/hints.php

and

http://www.simes.clara.co.uk/programs/sudoku.htm

Lastly, on how to find them: once you know what you're looking for, you just have to look I'm afraid. That's the fun, sometimes it takes a minute, sometimes 30.
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Postby Jeff » Sun Aug 21, 2005 4:55 pm

Karyobin wrote:1. I have never found, nor needed to use, a swordfish.

2. Ditto chains, though others here will disagree.


Totally agreed, only because either the puzzle is too trivial or when you find a grid that cannot be solved by x-wing or colours, you would go directly to forcing chains. But, can you describe a method to find forcing chains?
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Postby Karyobin » Sun Aug 21, 2005 5:09 pm

I suspect a challenge!

Truth is, I have never used a chain. Y'see, I am essentially a monumentally lazy puzzle-solver and as I've mentioned in other threads, my mission is not to find impossipuzzles, but to merely improve my observation skills (and thereby times) for Very Hards and Fiendish ones.

I am aware of the mechanics of chains, but have never bothered to sit down and read a thorough description of them, and therefore remain in a position of semi-luminescence as to their use.

To come to the nitty-gritty however, if you would seriously like me to try to identify a method for finding them (if indeed such a method exists, which I suspect it doesn't and will therefore accuse you of being a great big tease) then by all means point me to (a) a good source of puzzles which require them and (b) a good description of what they are and how they work, and I'll do my best.
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Postby Jeff » Sun Aug 21, 2005 5:25 pm

Calm down. This is not a chellege and difficult puzzles don't appear on papers every day.

Your reply answered the question already, ie. even the very hard or fiendish puzzles only require up to x-wing to solve. This is understandable, because my local paper publishes 5 star puzzles that don't even need x-wing to solve and sometimes with multiple solutions.

Tso and Scott are at the moment trying to describe a method to identify forcing chains, but it seems quite complicated.
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Thank you but what about?

Postby kleinman » Sun Aug 21, 2005 6:24 pm

I will try and work through what Jeff recommends, though I tend to agree with the view that they are not really needed.
Can anyone tell me what 'naked triples' are and can 'locked to a row' only be when a number can only be in 2 places in a box?
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Naked Triples

Postby Doyle » Sun Aug 21, 2005 11:45 pm

Naked Triples: This occurs when, in any one unit, there are three and only three cells that contain only the digits x,y,z. The simplest case would be three cells with the candidates (x,y,z), (x,y,z), (x,y,z), but there are other cases where one of the candidates is missing from one or more cells. For example, (x,y), (x,z), (y,z) is also a Naked Triple. When you have identified an NT, you then use it to eliminate x, y and z from all other cells in the unit. A most useful solving tactic, happens often.
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