Locked Pairs

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Locked Pairs

Postby rick.schneider » Sun Mar 09, 2008 9:21 pm

I am having trouble deciding which cells can be excluded for search values when using swordfish and jellyfish. I think this is because I don'r really know how to absolutely identify locked pairs. Doea anyone have a complete definition? Thanks.
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Postby ab » Sun Mar 09, 2008 11:53 pm

Not sure what you mean by locked pairs, but whatever it is it's got nothing to do with swordfish and jellyfish!

Swordfish occur when one candidate appears on only three columns in three rows. That candidate can then be eliminated from any other rows in those columns. You can also exchange rows and columns in the above definition. Jellyfish are defined in the same way but over four rows and columns.

It's explained more clearly here with some examples:
http://uk.geocities.com/aidan_001/
You'll find other explanations here:
http://forum.enjoysudoku.com/viewtopic.php?p=21804#p21804
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Postby rick.schneider » Mon Mar 10, 2008 3:09 am

ab: Thanks for the quick reply. I may have been misinformed, but I thought the reason you can do the eliminations is because of locked pairs -- the same principle that applies to some chains.

Anyway, some of the literature I have read on the subject refers to locked pairs. I thought if I could find an accurate definition of the term it would help me.

If anyone knows what I am talking about, please help. Clearly, I don't know!
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Postby daj95376 » Mon Mar 10, 2008 3:34 am

You'll find Locked Pair defined here http://www.sudopedia.org/wiki/Locked_Pair

Basically, think of the Naked Pair {12} in cells [r1c12]. The Naked Pair can cause eliminations in [r1] and [b1].

Code: Select all
 (*) cell eliminations for Locked Pair
 +-----------------------------------+
 | 12 12  *  |  *  *  *  |  *  *  *  |
 |  *  *  *  |  .  .  .  |  .  .  .  |
 |  *  *  *  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

I agree with ab that it doesn't have anything to do with fish.
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Locked Pairs

Postby rick.schneider » Mon Mar 10, 2008 5:09 am

Thanks, daj. I think I have been asking myself the wrong question.
In the following table, how can I tell which cells are part of the swordfish, and which can be eliminated. If I eliminate the small n's, it doesn't work, and I don't know why. Thanks for the help.
N n N

n N N


N N
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Re: Locked Pairs

Postby hobiwan » Mon Mar 10, 2008 7:16 am

rick.schneider wrote:Thanks, daj. I think I have been asking myself the wrong question.
In the following table, how can I tell which cells are part of the swordfish, and which can be eliminated. If I eliminate the small n's, it doesn't work, and I don't know why. Thanks for the help.
N n N

n N N


N N

Look here for a short explanation with examples.
I am not sure about your example, is it a swordfish in the rows or in the columns? If your swordfish looks like this:
Code: Select all
 +-----------------------------------+
 |  .  .  .  |  . .  .   |  .  .  .  |
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

it is a "swordfish in the rows". Rows 2, 4 and 8 are called the "base set" and candidates can never be eliminated from the base set. Since the candidates in those rows are in columns 2, 4 and 9, those columns are called the "cover set" and you can eliminate all candidates in the cover set, that are not part of the base set (in the above example all candidates marked with an asterisk):
Code: Select all
 +-----------------------------------+
 |  .  *  .  |  * .  .   |  .  .  *  |
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  *  .  |  *  .  .  |  .  .  *  |
 |-----------+-----------+-----------|
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  *  .  |  *  .  .  |  .  .  *  |
 |  .  *  .  |  *  .  .  |  .  .  *  |
 |-----------+-----------+-----------|
 |  .  *  .  |  *  .  .  |  .  .  *  |
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  *  .  |  *  .  .  |  .  .  *  |
 +-----------------------------------+


Edit: corrected my invalid fish diagrams according to Pat's post below
Last edited by hobiwan on Mon Mar 10, 2008 6:28 am, edited 2 times in total.
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re: Swordfish

Postby Pat » Mon Mar 10, 2008 8:10 am

hobiwan wrote:If your swordfish looks like this:
Code: Select all
 +-----------------------------------+
 |  .  .  .  |  . .  .   |  .  .  .  |
 |  .  X  .  |  X  .  .  |  .  .  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  X  .  |  X  .  .  |  .  .  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  X  .  |  X  .  .  |  .  .  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


it is a "swordfish in the rows". Rows 2, 4 and 8 are called the "base set". Since the candidates in those rows are in columns 2, 4 and 9, those columns are called the "cover set" and you can eliminate all candidates in the cover set, that are not part of the base set


a correction to hobiwan's post --
    the diagram as shown
    could be a Swordfish in rows
    and could be a Swordfish in columns
      a Swordfish is not determined by the cells where the digit can be,
      it is determined by the cells where the digit cannot be
from hobiwan's text, his diagram should've been --

Code: Select all
 +-----------------------------------+
 |  .  .  .  |  . .  .   |  .  .  .  |
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+



-- as he said, exclude the digit in columns 2,4,9 outside of rows 2,4,8
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Re: re: Swordfish

Postby hobiwan » Mon Mar 10, 2008 8:46 am

Pat wrote:a correction to hobiwan's post --
    the diagram as shown
    could be a Swordfish in rows
    and could be a Swordfish in columns
      a Swordfish is not determined by the cells where the digit can be,
      it is determined by the cells where the digit cannot be
from hobiwan's text, his diagram should've been --

Code: Select all
 +-----------------------------------+
 |  .  .  .  |  . .  .   |  .  .  .  |
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  /  X  /  |  X  /  /  |  /  /  X  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+



-- as he said, exclude the digit in columns 2,4,9 outside of rows 2,4,8

You are right of course, I really shouldn't do posts in five minute pauses without thinking anymore:(
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Locked Pairs

Postby rick.schneider » Mon Mar 10, 2008 4:46 pm

Fantastic! I was trying to remove candidates which are apparently part of the base set, which is a hit-or-miss proposition.

Thanks to all of you for your patience and kindness.
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