The New Sudoku Players' Forum

[aran]

David P Bird
I note your hypothetical objections to my hypothetical object !

I'm not sure that your stripped down version is much different to my own.
In your example
p cannot contain 1 nor 2 since you wouldn't have written p1 at r1c1 and p2 at r9c1.
but 1 and 2 will be singles unless they occur elsewhere
so q must contain 1 and 2
therefore the unsolved cells of your column 1 become
341 345712 34 345712 5712 342 which is not greatly dissimilar to my abc abd abce abc abcdex abcdx.

[David P Bird]

Aran, I think you have misread my post on your first point. I have no hypothetical objections to your hypothetical object at all, in fact that you managed to compose it is admirable! That's why I built up my stripped down version of it.

But now I must apologise for mistakenly editing out two instances of (12) just as I was posting my piece, which I've now restored.
Repeated:

Code: Select all

|---------|-------|---------|
| p1  . . | . . . | . . x1  |   RCCs = 1 & 2
| pq  . . | . . . | . . y12 |   
| 6   . . | . . . | . . 7   |   p = 3 and/or 4   (1234)ANS:r149c1
|---------|-------|---------|   q = 5 and/or 7   (57+1234)AHS:r267c1
| p   . . | . . . | . . 8   |   
| 9   . . | . . . | . . xy  |   x = 4 and/or 5   (1245)ANS:r169c9
| pq  . . | . . . | . . x   |   y = 6 and/or 9   (69+1245)AHS:r258c9
|---------|-------|---------|
| q12 . . | . . . | . . 3   |
| 8   . . | . . . | . . xy  |
| p2  . . | . . . | . . x2  |
|---------|-------|---------|

(134=234)r1c9c1 – (245=145)r169c9 – Loop => r26c1> 34, r58c9 <> 45, r1c2345678 <> 1, r9c2345678 <> 2

My reasoning was that there can only be one of each in the ANSs because if there were more there would be alternative cells where they could be true and the weak links in rows 1 & 9 wouldn't necessarily follow (as your original description showed).

If the AHSs were extended to include some of the cells I've shown as solved, then (12) could be added to those as well, but they couldn't exist together in any other cells containing p in c1 or x in c9.

My conclusion was that although your hypothetical DL-ANSs could exist, there would generally be a variety of other ways the eliminations could be made.

[aran]

David P Bird
I did realise that you were observing and not objecting...I just couldn't quite resist the juxtaposition of "hypothetical objections" and "hypothetical objects"...and should have made that clear