The New Sudoku Players' Forum

[Sped]

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?

[MCC]

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

[Sped]

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?

[vidarino]

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

[Sped]

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?

[vidarino]

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.

There's a lot more info about XY-Chains here.

Vidar

[Sped]

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.