## Locked Pairs

Post the puzzle or solving technique that's causing you trouble and someone will help

### Locked Pairs

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.
rick.schneider

Posts: 4
Joined: 09 March 2008

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
ab

Posts: 451
Joined: 06 September 2005

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.

rick.schneider

Posts: 4
Joined: 09 March 2008

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.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Locked Pairs

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
rick.schneider

Posts: 4
Joined: 09 March 2008

### Re: Locked Pairs

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.
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

### re: Swordfish

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

Pat

Posts: 3523
Joined: 18 July 2005

### Re: re: Swordfish

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
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

### Locked Pairs

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.
rick.schneider

Posts: 4
Joined: 09 March 2008