## Is this a valid exclusion?

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### Is this a valid exclusion?

Based on the following loop, marked with asterisks in the grid, I excluded 3s from the non-asterisked cells in columns 4 and 9

(r9c4)-3-(r3c4)-8-(r3c9)-3-(r9c9)-4-(r9c4)

Code: Select all
` *-----------------------------------------------------------* | 9     3     26    | 7     56    58    | 4     28    1     | | 26    8     1     | 9     36    4     | 7     23    5     | | 5     7     4     | 38*   2     1     | 6     9     38*   | |-------------------+-------------------+-------------------| | 1     9     8     | 6     4     7     | 3     5     2     | | 2367  5     2367  | 23    1     39    | 8     4     79    | | 237   4     237   | 2358  35    3589  | 1     6     79    | |-------------------+-------------------+-------------------| | 34    1     9     | 345   8     35    | 2     7     6     | | 347   2     37    | 1     9     6     | 5     38    348   | | 8     6     5     | 34*   7     2     | 9     1     34*   | *-----------------------------------------------------------*`

Is this a valid exclusion, and if so, what is this technique called?
Sped

Posts: 126
Joined: 26 March 2006

The 3's in the cells you marked make a x-wing.

Either r3c4 and r9c9 contain a 3 or,
r9c4 and r3c9 contain a 3.
Therefore you can eliminate the 3's in r5c4, r6c4, r7c4, r8c9.

MCC
MCC

Posts: 1275
Joined: 08 June 2005

MCC wrote:The 3's in the cells you marked make a x-wing.

Either r3c4 and r9c9 contain a 3 or,
r9c4 and r3c9 contain a 3.
Therefore you can eliminate the 3's in r5c4, r6c4, r7c4, r8c9.

MCC

Now that you point it out, I see the X Wing on threes, so the exclusions are valid.

However, had there been 3s elsewhere in rows 3 and nine, messing up the X wing, could the exclusions still be made based on the loop of the 4 bivalue cells? i.e. exclude 3s from columns 4 and 9, 8s from row 3, and 4s from row 9?
Sped

Posts: 126
Joined: 26 March 2006

Sped wrote:However, had there been 3s elsewhere in rows 3 and nine, messing up the X wing, could the exclusions still be made based on the loop of the 4 bivalue cells? i.e. exclude 3s from columns 4 and 9, 8s from row 3, and 4s from row 9?

Yep, those four corner cells also form an XY-Chain, that allows you to eliminate candidates "along the edges", so to speak. It's there regardless of the X-Wing, so feel free to do the eliminations right now.

Vidar
vidarino

Posts: 295
Joined: 02 January 2006

vidarino wrote:
Yep, those four corner cells also form an XY-Chain, that allows you to eliminate candidates "along the edges", so to speak. It's there regardless of the X-Wing, so feel free to do the eliminations right now.

Vidar

Great!

Generalizing,.. would it be true that a continuous XY chain can be any length, and need not be a rectangle?

Can the candidate common to adjacent links in the chain be excluded from all other cells sharing a group with both links?

Is that how it works?
Sped

Posts: 126
Joined: 26 March 2006

Sped wrote:Generalizing,.. would it be true that a continuous XY chain can be any length, and need not be a rectangle?

Can the candidate common to adjacent links in the chain be excluded from all other cells sharing a group with both links?

Is that how it works?

That is precisely how it works.

Vidar
vidarino

Posts: 295
Joined: 02 January 2006

Thanks for your help. I think I have XY Chains down now. Next I will try to get a handle on the whole nice loop thing.
Sped

Posts: 126
Joined: 26 March 2006

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