The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..6|4.1|...|
 |.3.|85.|...|
 |27.|.9.|...|
 |---+---+---|
 |.95|.3.|..6|
 |..8|...|3..|
 |6..|.8.|94.|
 |---+---+---|
 |...|.7.|.18|
 |...|.69|.3.|
 |...|2.8|6..|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 58    58    6      | 4     2     1      | 7     9     3      |
| 149   3     149    | 8     5     7      | 124   6     124    |
| 2     7     14     | 6     9     3      | 1458  58    145    |
|--------------------+--------------------+--------------------|
|d147   9     5      |c17    3    a24     | 18    278   6      |
| 147   124   8      | 9    b14    6      | 3     257   157    |
| 6    e12    3      | 157   8     5-2    | 9     4     17     |
|--------------------+--------------------+--------------------|
| 459   6     249    | 3     7     45     | 245   1     8      |
| 1458  1458  1247   | 15    6     9      | 245   3     2457   |
| 3     145   147    | 2     14    8      | 6     57    9      |
*--------------------------------------------------------------*

(2=4*) r4c6 - (4=1)r5c5 - (1=7*) r4c4 - (47*=1) r4c1 - (1=2) r6c2 => - 2 r6c6; lclste

Leren

[daj95376]

_

I am not criticizing Leren's solution. I'm only using it as an example of what I call selective memory in some networks.

Selective Memory: remembering only some of the eliminations associated with network assignments.

Here's the grid after Leren's first four assignments:

Code: Select all

 *-------------------------------------------------------------*
 |  58    58    6     |  4     2     1     | 7     9     3     |
 |  49    3     149   |  8     5     7     | 124   6     124   |
 |  2     7     14    |  6     9     3     | 1458  58    145   |
 |--------------------+--------------------+-------------------|
 | d1     9     5     | c7     3    a4     | 8     28    6     |
 |  47    24    8     |  9    b1     6     | 3     257   57    |
 |  6    *2     3     | *5     8    *25    | 9     4    #17    |
 |--------------------+--------------------+-------------------|
 |  459   6     249   |  3     7     5     | 245   1     8     |
 |  458   1458  1247  |  15    6     9     | 245   3     2457  |
 |  3     145   147   |  2     4     8     | 6     57    9     |
 *-------------------------------------------------------------*


You'll notice that there's a contradiction -- r6c246=25 or r6c9=17 -- in [r6] at this point.

So, an alternate step might be:

Code: Select all

 4*r4c6 - (4=1)r5c5 - (1=7)r4c4 - (*47=1)r4c1 ; contradiction [r6]  =>  -4 r4c6


_

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 58    58    6     | 4     2     1     | 7     9     3     |
 | 149   3     149   | 8     5     7     | 124   6     124   |
 | 2     7     14    | 6     9     3     | 1458  58    145   |
 *-------------------+-------------------+-------------------|
 |a147   9     5     |b17    3    d24    | 18    278   6     |
 | 147   124   8     | 9    c14    6     | 3     257   157   |
 | 6     12    3     | 157   8     5-2   | 9     4     17    |
 *-------------------+-------------------+-------------------|
 | 459   6     249   | 3     7     45    | 245   1     8     |
 | 1458  1458  1247  | 15    6     9     | 245   3     2457  |
 | 3     145   147   | 2     14    8     | 6     57    9     |
 *-----------------------------------------------------------*

Another way to look at it is an Almost XY-wing:

[XY-wing 1/2/4 pr4c1, wr4c6,r6c2]           => -2 r6c6
 ||
(7)r4c1 - (7=1)r4c4 - (1=4)r5c5 - (4=2)r4c6 => -2 r6c6



[daj95376]

Another way to look at it is an Almost XY-wing:

[XY-wing 1/2/4 pr4c1, wr4c6,r6c2] => -2 r6c6
||
(7)r4c1 - (7=1)r4c4 - (1=4)r5c5 - (4=2)r4c6 => -2 r6c6

Hmmm!!!

After your third assignment, there's the contradiction that you've eliminated all of the 4s in [b4]. It sometimes gets tricky when you try to not create a contradiction following a false assumption. Especially when all of the cells/candidates are in the same chute (band/stack).

_

[blue]

Here's a short list of (related) Almost XY-Wing eliminations:

Potential XY-Wing with:

pivot: (14)r4c1
pincers: (12)r6c2, (24)r4c6
eliminating: 2r6c6
extra candidate(s): 7r4c1 (in the pivot cell)

1) 5r6c6 = (5-7)r6c4 = 7r4c4 - 7r4c1 = (XY-Wing: (14)r4c1,(12)r6c2,(24)r4c6) => r6c6<>2; lcstte
2) 7r6c4 = r4c4 - 7r4c1 = (XY-Wing: (14)r4c1,(12)r6c2,(24)r4c6) - (2=5)r6c6 => r6c4<>5; lcstte

Potential XY-Wing with:

pivot: (17)r4c4
pincers: (47)r4c1, (14)r5c5
eliminating: 4r4c6
extra candidate(s): 1r4c1 (in a pincer cell - r4c1)

3) 2r4c6 = r6c6 - (2=1)r7c2 - 1r4c1 = (XY-Wing: (17)r4c4,(47)r4c1,(14)r5c5) => r4c6<>4; lcstte
4) (2=1)r6c2 - 1r4c1 = (XY-Wing: (17)r4c4,(47)r4c1,(14)r5c5) - (4=2)r4c6 => r6c6<>2; lcstte
5) 1r4c1 = (XY-Wing: (17)r4c4,(47)r4c1,(14)r5c5) - (4=2)r4c6 - r6c6 = 2r6c2 => r6c2<>1; lcstte

[blue]

Hmmm!!!

(...)

Just a quick comment, since you''ve noticed this kind of thing before.

(Almost) any time someone shows a strong link in an AIC (or AIC-like network), one end or another is going to be false in the actual solution. The only thing left to question, is how hard you might need to work, to see which end is actually false. Sometimes, other links in the AIC itself, will show an answer. When you put that kind of thing into XSudo, it will show up as a "cannibal elimination". More often than not, you would need to supply additional information to show off the (percieved) problem. In this case, it would be a strong link for 4b4, and a weak link for 4r5. It's nothing to be concerned about.

Cheers,
Blue.

[SteveG48]

Hmmm!!!

(...)

Just a quick comment, since you''ve noticed this kind of thing before.

(Almost) any time someone shows a strong link in an AIC (or AIC-like network), one end or another is going to be false in the actual solution. The only thing left to question, is how hard you might need to work, to see which end is actually false. Sometimes, other links in the AIC itself, will show an answer. When you put that kind of thing into XSudo, it will show up as a "cannibal elimination". More often than not, you would need to supply additional information to show off the (percieved) problem. In this case, it's be a strong link for 4b4, and a weak link for 4r5. It's nothing to be concerned about.

Cheers,
Blue.

Agreed. If you look on a chain as being implied assignments (and most of us tend to do that), then you're bound to get frequent contradictions. If you think of the chain as being just strong and weak links, then it doesn't bother you. Just the other day I posted a solution in which the candidate I ultimately eliminated was implied as "true" in the middle of the chain. That's because the implied assumption at the start of the chain turned out to be false in the final solution.

[daj95376]

Just a quick comment, since you''ve noticed this kind of thing before.

(Almost) any time someone shows a strong link in an AIC (or AIC-like network), one end or another is going to be false in the actual solution.

I'm sorry to be atop an old soap box. Especially since my issue with networks doesn't seem to negatively affect the outcome.

As for true/false on endpoints, now you've opened Pandora's Box ... a little.

In the actual solution for this puzzle, both r4c6=2 and r6c2=2 are true. In fact, there is a cycle on <2> in [band 2], and simple coloring forces r4c6 and r6c2 to either be both true or both false. However, Leren's network assumes r4c6<>2 and derives r6c2=2 ... in direct contradiction to simpler analysis. Don't you find that interesting/confusing!!!

I've learned to accept that AICs can turn a false assumption into a true deduction because (typically) a weak link will transition the logic from a false sequence to a true sequence. In Leren's network, the false sequence extends from r4c6 to r4c1 and then transitions to the true sequence with the weak link "-(1=2)r6c2".

I'm not comfortable in dealing with a network stream that only remembers the eliminations that "help" it reach the desired conclusion.

Again, my apologies for bringing up an old soap box topic.

BTW: Do you have an example of an Almost XY-Wing where the extra candidate (in the pivot cell) is true in the solution?

_

[SteveG48]

In the actual solution for this puzzle, both r4c6=2 and r6c2=2 are true. In fact, there is a cycle on <2> in [band 2], and simple coloring forces r4c6 and r6c2 to either be both true or both false. However, Leren's network assumes r4c6<>2 and derives r6c2=2 ... in direct contradiction to simpler analysis. Don't you find that interesting/confusing!!!

Not really. Leren's network establishes a strong link between r4c6 and r6c2, meaning (of course) that if r4c6 is false then r6c2 is true and the reverse- if r6c2 is false then r4c6 is true. The simpler analysis shows that both are true or both are false. There's no contradiction in that. The only condition that satisfies both analyses is that both are true, and that's the answer to the puzzle. A strong link doesn't always imply that one is true and one is false; both true is also a possibility.

[blue]

BTW: Do you have an example of an Almost XY-Wing where the extra candidate (in the pivot cell) is true in the solution?

I don't, but I'll try to produce one.

Again, my apologies for bringing up an old soap box topic.

No need to apologize. Casting new light on old situations can be ... enlightening(!) ... at times.
In fact, your earlier analysis of Leren's solution, shows that there's a 2-step solution using smaller patterns:
1) (7=1)r4c4 - (1=4)r5c5 - r5c12 = 4r4c1 => r4c1<>7
2) XY-Wing (14)r4c1,(12)r6c2,(24)r4c6 => r6c6<>2 (typo corrected)

In the actual solution for this puzzle, both r4c6=2 and r6c2=2 are true. In fact, there is a cycle on <2> in [band 2], and simple coloring forces r4c6 and r6c2 to either be both true or both false. However, Leren's network assumes r4c6<>2 and derives r6c2=2 ... in direct contradiction to simpler analysis. Don't you find that interesting/confusing!!!

Interesting because of the paradoxical ring to it, the way it's phrased. But then Leren's network can be extended on the right by "- 2r6c6 = 2r4c6", to give a "2r4c6 = (...) = 2r4c6" thing that apparently "assumes r4c6<>2 and derives r4c6=2".

If you look on a chain as being implied assignments (and most of us tend to do that), then you're bound to get frequent contradictions. If you think of the chain as being just strong and weak links, then it doesn't bother you.

I guess I'm firmly in the 2nd camp here.

I'm not comfortable in dealing with a network stream that only remembers the eliminations that "help" it reach the desired conclusion.

I'm a little uncomfortable with "memory" in the first place. When it's used to show that a particular assumption leads to a contradiction, I don't have a problem with it at all. In fact, it seems necessary. When it's used in something with strong links on both ends, I prefer the logic in the left/right reversal ... where strong links can "fork", and weak links "converge" on candidates that need to be "remembered" in the other view. It requires a more complicated diagram, though, so I'm flexible.

[daj95376]

_

Steve and blue,

Good points all around. I'll try to stay off my soap box the next time I notice that a network sequence creates a contradiction before it reaches its conclusion. For sure, I'll be guilty of posting such sequences myself.


Regards, Danny

_

[SteveG48]

I'll try to stay off my soap box the next time I notice that a network sequence creates a contradiction before it reaches its conclusion.

I hope not! The puzzles are fun, but the technical discussions are what it's all about- IMO, of course.

[DonM]

(Almost) any time someone shows a strong link in an AIC (or AIC-like network), one end or another is going to be false in the actual solution. The only thing left to question, is how hard you might need to work, to see which end is actually false. Sometimes, other links in the AIC itself, will show an answer. When you put that kind of thing into XSudo, it will show up as a "cannibal elimination"...

Cheers,
Blue.

At first, I was thinking that: Both ends of an AIC going to be false in most actual solutions? Isn't that what discontinuities are all about? Then I realized that you were likely talking about the information available following the full puzzle solution. But then, understanding that, I was wondering what kind of point you were trying to make. I'm not seeing it. Also, what is a 'cannonball elimination'?

Agreed. If you look on a chain as being implied assignments (and most of us tend to do that), then you're bound to get frequent contradictions. If you think of the chain as being just strong and weak links, then it doesn't bother you. Just the other day I posted a solution in which the candidate I ultimately eliminated was implied as "true" in the middle of the chain. That's because the implied assumption at the start of the chain turned out to be false in the final solution.

I'm not understanding what the point is here either. I think of 'to imply' as 'to suggest' so if I create an AIC looking at it as strong & weak links, I am 'implying' assignments as opposed to proposing 'actual assignments'. In any event, how does looking at a chain as being 'implied assignments' get you more frequent contradictions than thinking of a chain 'as being just strong and weak links'?

[SteveG48]

Agreed. If you look on a chain as being implied assignments (and most of us tend to do that), then you're bound to get frequent contradictions. If you think of the chain as being just strong and weak links, then it doesn't bother you. Just the other day I posted a solution in which the candidate I ultimately eliminated was implied as "true" in the middle of the chain. That's because the implied assumption at the start of the chain turned out to be false in the final solution.

I'm not understanding what the point is here either. I think of 'to imply' as 'to suggest' so if I create an AIC looking at it as strong & weak links, I am 'implying' assignments as opposed to proposing 'actual assignments'. In any event, how does looking at a chain as being 'implied assignments' get you more frequent contradictions than thinking of a chain 'as being just strong and weak links'?

What I meant was that if you imply (or suggest) that a candidate has a certain value, then your suggestion may be wrong, in which case you may see contradictions. If, however, you regard the chain as simply establishing a link between the cells at the two ends of the chain, then it means only that if one end has a certain value then we would conclude something about the other end. There is no suggestion that the starting end of the chain actually has a particular value.