The New Sudoku Players' Forum

[bennys]

Code: Select all

+-----------+
|           |
| 34        |
| 12 123    |
+-----------+
| 14        |
|           |
|           |
+-----------+


Here in the upper box we cant have 2 in all the unmarked cells.

[Cec]

Here in the upper box we cant have 2 in all the unmarked cells.

Hi bennys,

I'm confused with this post. The subject title suggests you might be asking which is the best way to submit a grid puzzle!. Is this your question? Also, are the ... shown in the following box the "unmarked cells" you refer to in the upper box?

... ... ...
34 ... ...
12 123 ...

Cec

[angusj]

I'm confused with this post. The subject title suggests you might be asking which is the best way to submit a grid puzzle!.

It's a tad cryptic but he is posting another solving technique - though it's not obvious to spot.

Anyhow, take the 2 out of the above cells (on the premise it's assigned to another cell in the top box) and it's quickly apparent that there'd be no solution. Therefore the 2 must be in one of the two cells indicated.

[r.e.s.]

bennys,
That seems to involve the same kind of forcing net as described in "Snippet #2" <here>.

[Cec]

"...Anyhow, take the 2 out of the above cells (on the premise it's assigned to another cell in the top box) and it's quickly apparent that there'd be no solution. Therefore the 2 must be in one of the two cells indicated.

Thanks Angusj. for your prompt reply. Trying to explain my confusion has now become too hard so I better not try - if it's a new technique I will put it on the "back-burner" until I'm more capable with the "basic" techniques discussed in this forum.

Regards, Cec

[rubylips]

It's possible to view the pattern as two Almost Disjoint Subsets - one in r3c1 and r3c2, the other trivially in r4c1 - with a link cell at r2c1. When the link cell contains a 3, the values 1, 2 and 3 are excluded from the unlabelled cells in Box 1 - when it contains a 4, the values 1 and 4 are excluded from Column 1 except for the cells r2c1 and r4c1. The intersection of these two exclusion zones is the cell r1c1, which cannot contain the value 1. (bennys doesn't mention this result).

We've seen this result in several threads now (e.g. I didn't see this argument used before) but the situation here is complicated by the fact that r3c1, one of the cells in an Almost Disjoint Subset, lies inside the intersection area, which means that when r2c1 contains a 4, the value 1 is excluded from r3c1, which forces the cell to contain a 2. This extends the list of eliminations common to both link cell settings to 1 excluded from r1c1 and 2 excluded from all unlabelled cells.

[tso]

This pattern is to an XYZ wing as an XYZ wing is to an XY wing. This and several variations have been discussed here and here.

[bennys]

What about this one?

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+------------+
| .  1234  . |
|234  235  . |
|2345  .   . |
+------------+
| .  1357  . |
| .  1357  . |
| .  1357  . |
+------------+

[rubylips]

The link cell is r1c2.

When r1c2=123, we have a Disjoint Subset in Column 2 in the values 1, 2, 3, 5 and 7, which excludes the 2 from unlabelled cells in Box 1, the 7 from unlabelled cells in Box 4 and all the values from unlabelled cells in Column 2.

When r1c2=4, we have a Disjoint Subset in Box 1 in the values 2, 3, 4 and 5, which excludes these values from the unlabelled cells in the Box.

The mutual exclusions are 2 from the unlabelled cells in Box 1 and 3 and 5 from r3c2.

[bennys]

Rubylips, did you implemented that kind of arguments in your solver?
In what priority they are?

[rubylips]

Not yet - though it does consider classic Two Sector Disjoint Subsets. I'd like to establish a highly general form of the new technique before I implement it.

[Jeff]

Code: Select all

+-------------+
| .    .    . |
| .    .    . |
| .    .   17 |
+-------------+
| .    .   47 |
| .    .    . |
| .    .  1357|
+-------------+
| .    .  1357|
|135  15   345|
| .    .    . |
+-------------+

Rubylips, the disjoint subset argument certainly has the advantage of drawing more general conclusions for the whole sector rather than just one digit and one cell at a time.

With the above candidate grid, the following deductions were made through the argument of empty cell contradition:

Target cell: r7c3=1357

Forcing net:
r3c3=7 => r7c3<>7
r3c3=7 => r4c3=4 => r8c3=35 (Naked triple with r8c1 & r8c2) => r7c3<>135
Therefore r3c3<>7 => r3c3=1

Forcing net:
r6c3=7 => r7c3<>7
r6c3=7 => r4c3=4 => r8c3=35 (Naked triple with r8c1 & r8c2) => r7c3<>135
Therefore r6c3<>7

Could you advise how the same deductions can be made through the argument of disjoint subsets.

[bennys]

I think that R6C3 is not relevant here
The only candidates for 7 in C3 are R7C3 and R4C3.

[Jeff]

Thanks benny, the outcome of the contradiction is r6c3<>7 so that the 7 in r6c3 can be eliminated. After that, the only places for 7 in col 3 are indeed r4c3 and r7c3.