The New Sudoku Players' Forum

[Luke]

However, I'm curious about your "tidying up". From your previous position, after singles, pairs, locked candidates and an xy-wing I can almost reach that position barring an elimination of 4 from r2c2. It will be much appreciated if you can elaborate how you eliminated that 4 from r2c2.

I pencil solve, so I haven't a readout to back check. There definitely was a wing on [478] in c12 and then a UR right in the same area that took out the 4 in r2c2. When time allows (read: not supposed to be working) I'll see if I can find it again.

My definition of tidiness might be more liberal than others .

[Edit: add PM] UR on [45], w/x-wing overlay:

Code: Select all

*--------------------------------------------------------------------*
 | 3      48     28     | 468    5      1      | 9      7      268    |
 |*2457  -458    6      | 478    9      3478   | 28     34     1      |
 | 47     9      1      | 4678   2      34678  | 5      34     68     |
 |----------------------+----------------------+----------------------|
 | 6      78     578    | 289    4      289    | 12     159    3      |
 | 9      2      4      | 3      1      5      | 6      8      7      |
 | 1      3      58     | 2689   7      2689   | 24     59     245    |
 |----------------------+----------------------+----------------------|
 |*45    *457    3      | 1479   6      479    | 148    2      48     |
 | 8      6      9      | 124    3      24     | 7      15     45     |
 | 24     1      27     | 5      8      47     | 3      6      9      |
 *--------------------------------------------------------------------*

[daj95376]

Okay, I'll try to be more supportive than a hindrance. Here's what I see in your approach.

You rely on finding a rectangular arrangement of cells, with an ALS conjugate relationship using bivalue cells on one side, and a strong link on the opposite side for one of the non-common values in the ALS.

Code: Select all

________________________________________________________________________________________

 1) strong link:    [r5c9]=2=[r1c9]                              in [c9]
 2) bivalue ALS:                    2-[r1c3]-8-[r6c3]-5          in [c3]
 3) missing:      5=               -                   -[r5c9]   to make it a chain/loop
 +-----------------------------------------------------------------------+
 |  3      48     28     |  468    5      1      |  9      7      2468   |
 |  2457   4578   6      |  478    9      3478   |  2348   34     1      |
 |  47     9      1      |  4678   2      34678  |  5      346    468    |
 |-----------------------+-----------------------+-----------------------|
 |  67     678    578    |  289    4      289    |  12     159    3      |
 |  9      2      4      |  3      1      5      |  6      8      7      |
 |  1      3      58     |  2689   7      2689   |  24     59     245    |
 |-----------------------+-----------------------+-----------------------|
 |  457    457    3      |  1479   6      479    |  148    2      458    |
 |  8      456    9      |  124    3      24     |  7      15     456    |
 |  2467   1      27     |  5      8      47     |  34     346    9      |
 +-----------------------------------------------------------------------+
 # 86 eliminations remain


It appears to be pretty simple. Placing the "right" value in the "right" cell of the strong link produces a contradiction with the ALS.

I think your name is completely inappropriate for what's happening.

===== ===== ===== ===== ===== ===== ===== Note

It appears to me that any ALS based on bivalue cells can be used on one side, just as long as the end cells of the chain align with the strong link ... and with a value in common. The ALS endpoint cells don't even need to be in the same unit.

[ronk]

I think your name is completely inappropriate for what's happening.

It's difficult to be sure to what or to whom you refer, but I think udosuk's hybrid wing term in the title of this thread is a pretty good one.

There are several useful combinations of three strong inferences and we've got names (xy-wing, w-wing, and maybe others) for some of them, but I wouldn't like to see a separate name for every one. Hybrid is a catch-all term that implies an arbitrary mix of bivalues and bilocals and hybrid-wing, or even h-wing, wouldn't carry the baggage that the y-wing term did.

[udosuk]

Luke, thanks for the elaboration. I should have thought of something along the uniqueness line since I specifically requested it.

Ron, thanks for your kind words. You have pretty much explained my choice of the word "hybrid" perfectly.

Added later:

Here are some examples of my system of "wings", including the classical XY-Wing, Strong-Wing and 4 different versions of Hybrid-Wings:

XY-Wing (aka Weak-Wing ) with 4 weak links

Code: Select all

xy - xz
|     |
yz -  can't be z

Strong-Wing with 4 strong links

Code: Select all

?  =x=  ?
||     ||
y       w
||     ||
?  =z=  must be w or z

Hybrid-Wing with 3 weak links + 1 strong link (as cited by me on p.1)

Code: Select all

xy -  ?
|    ||
|     x
|    ||
yz -  can't be z

Hybrid-Wing with 1 weak link + 3 strong links (as cited by Luke on p.1)

Code: Select all

?  =x=  ?
||     ||
y       w
||     ||
?  ---  can't be y

Hybrid-Wing with 2 weak links + 2 strong links

Code: Select all

xy ---  ?
|      ||
|       x
|      ||
?  =y=  must be x or y

Hybrid-Wing with 2 weak links + 2 strong links

Code: Select all

?  =x= vz
||      |
y       |
||      |
vw ---  can't be v

[aran]

You appear to be putting weak links and strong links on a par, and of seeing symmetries where there are none.
Weaks links don't exist in a vacuum, strong links do.
To describe a traditional XY-wing as 4 weak links is IMO not too useful since to have any meaning, it also requires specifying a start point, a candidate and a state : suppose z true in cell C.
On the other hand, to see an XY-wing as a strong link on z across the diagonal requires no specs and sets up the elimination.

[udosuk]

Each strong link is tagged with a candidate value, while each weak link doesn't need to be expressed with an explicit value in the diagrams, just the cells at the ends of it has to be bivalued or involving in some ALS. So both of them are associated to values, and do not "exist in a vacuum".

And I'm not the first one comparing strong links and weak links together. See this link.

[ronk]

Here are some examples of my system of "wings", including the classical XY-Wing, Strong-Wing and 4 different versions of Hybrid-Wings:

...

Strong-Wing with 4 strong links

Code: Select all

?  =x=  ?
||     ||
y       w
||     ||
?  =z=  must be w or z

When w<>z, it's a Strong Ring, a different bird.

Code: Select all

A  =x=  B
||     ||
y       w
||     ||
D  =z=  C ==> A=xy, B=wx, C=wz, D=yz

I haven't look closely at the rest.

[aran]

Each strong link is
tagged with a candidate value, while each weak link doesn't need to be expressed with an explicit value in the diagrams, just the cells at the ends of it has to be bivalued or involving in some ALS. So both of them are associated to values, and do not "exist in a vacuum".

And I'm not the first one comparing strong links and weak links together. See this link.

Look at it like this then (using ab ac bc and cxxx as the XY wing corners)
Is there a well-defined strong link ?
Yes, c on the diagonal.
Does it do anything ?
Yes eliminates c in the far corner.

Is there a well defined weak link ?
Well there are lots :
a/a one way, then the way back
b/b one way then the way back
c/c one way, then the way back
c/c the other way then the way back.
Right, well let's see, does any of them do anything ?
a/a...no, neither way; b/b...no, neither way
c/c...no one way, both cases
But hold on, if both cases c/c the other way are combined, there looks to be an oddity. Yes a contradiction.
So we can eliminate c in the far corner.

[Luke]

I think there is value here as far as pattern recognition is concerned.

Just started this one today and here's the first thing I noticed:

Code: Select all

Ruud's Nightmare, Sat Dec 29,2007
007260001300007600000900003409500000010000030000008204200005000006100005100076800

 *--------------------------------------------------------------------*
 | 589    4589   7      | 2      6      3      | 49     4589   1      |
 | 3      24589  12458  | 48     1458   7      | 6      24589  289    |
 | 568    24568  12458  | 9      1458   14     | 47     24578  3      |
 |----------------------+----------------------+----------------------|
 | 4      2678   9      | 5      3      12     | 17     1678   678    |
 | 678    1      28     | 67    *249   *249    | 5      3      6789   |
 | 567    3567   35     | 67     19     8      | 2      19     4      |
 |----------------------+----------------------+----------------------|
 | 2      34789  348    | 348    489    5      | 13479  14679  679    |
 | 789    34789  6      | 1     *2489  *249    | 3479   479    5      |
 | 1      3459   345    | 34     7      6      | 8      249    29     |
 *--------------------------------------------------------------------*


Before the "Strong Wing" discussions I wouldn't have glanced at this and said, "Oh. r8c5=2."

[Luke]

This is a pretty interesting move, to me at least (highlight mine):

Code: Select all

+----------------------+----------------------+----------------------+
| 3      48     28     | 468    5      1      | 9      7      2468   |
| 2457   4578   6      | 478    9      3478   | 2348   34     1      |
| 47     9      1      | 4678   2      34678  | 5      346    468    |
+----------------------+----------------------+----------------------+
| 67     678    578    | 289    4      289    | 12     159    3      |
| 9      2      4      | 3      1      5      | 6      8      7      |
| 1      3      58     | 2689   7      2689   | 24     59     245    |
+----------------------+----------------------+----------------------+
| 457    457    3      | 1479   6      479    | 148    2      458    |
| 8      456    9      | 124    3      24     | 7      15     456    |
| 2467   1      27     | 5      8      47     | 34     346    9      |
+----------------------+----------------------+----------------------+

59r46c8=1r4c8-(1=2)r4c7-(2=89)r4c46-(8=67)r4c12-(78=5)r4c3-(5=8)r6c3-(8=2)r1c3-2r1c9=(2-5)r6c9 : =><5>r6c9.

This link would have never occurred to me because I didn't see how the hidden pair (67) forms a weak inference with (78). If it was (67)-(7=5) that would make sense (to me).

Now I think I've figured out what's really going on (famous last words.) The 8 in (78) is already "out" after the earlier (2=89)r4c46 . Is it the same concept that came up in this situation recently? Can any candidate in a previous strong link be considered eliminated in any particular chain as that chain is propagated?

[aran]

This is a pretty interesting move, to me at least (highlight mine):

Code: Select all

+----------------------+----------------------+----------------------+
| 3      48     28     | 468    5      1      | 9      7      2468   |
| 2457   4578   6      | 478    9      3478   | 2348   34     1      |
| 47     9      1      | 4678   2      34678  | 5      346    468    |
+----------------------+----------------------+----------------------+
| 67     678    578    | 289    4      289    | 12     159    3      |
| 9      2      4      | 3      1      5      | 6      8      7      |
| 1      3      58     | 2689   7      2689   | 24     59     245    |
+----------------------+----------------------+----------------------+
| 457    457    3      | 1479   6      479    | 148    2      458    |
| 8      456    9      | 124    3      24     | 7      15     456    |
| 2467   1      27     | 5      8      47     | 34     346    9      |
+----------------------+----------------------+----------------------+

59r46c8=1r4c8-(1=2)r4c7-(2=89)r4c46-(8=67)r4c12-(78=5)r4c3-(5=8)r6c3-(8=2)r1c3-2r1c9=(2-5)r6c9 : =><5>r6c9.

This link would have never occurred to me because I didn't see how the hidden pair (67) forms a weak inference with (78). If it was (67)-(7=5) that would make sense.

Now I think I've figured out what's really going on (famous last words.) The 8 in (78) is already "out" after the earlier (2=89)r4c46 . Is it the same concept that came up in this situation recently? Can any candidate in a previous strong link be considered eliminated in any particular chain as that chain is propagated?

Exactly right.
Call it "memory" : chains are perfectly logically entitled to remember anything previously "placed" in the chain by a preceding strong link.
I have come to the conclusion that any attempt to signal that memory has been used is either too cumbersome or too ugly, or both.
At one stage I used an asterisk with a footnote, at another an asterisk without any footnote.
Then (in the example you linked to) there was the # symbol recalling the placed candidate/cell ref being used again.
One or two of those in isolation might be fine, but in any numbers I think will lead ironically to loss of clarity (not to mention their powers of boredom).
Why it's almost insulting to anyone possibly interested in the chain to assume that he can't recall what's gone before

[Luke]

Thanks, aran. You've helped me go from a vague awareness of this to being able to start implementing it.

It's probably just me, but it seems memory use in chains is under-utilized. I don't notice many references to it in the forums or in educational material (web sites, tutorials, etc.)

I've learned many of the basics about chains by seeing how different solvers (computer programs, not humans) handle them. Is "memory" implemented into solving programs? It doesn't seem to be in the ones I use, unless of course I've been misusing them.

[hobiwan]

It's probably just me, but it seems memory use in chains is under-utilized. I don't notice many references to it in the forums or in educational material (web sites, tutorials, etc.)

I've learned many of the basics about chains by seeing how different solvers (computer programs, not humans) handle them. Is "memory" implemented into solving programs? It doesn't seem to be in the ones I use, unless of course I've been misusing them.

Isnt "chain memory" usually called "net"?

[aran]

It's probably just me, but it seems memory use in chains is under-utilized. I don't notice many references to it in the forums or in educational material (web sites, tutorials, etc.)

I've learned many of the basics about chains by seeing how different solvers (computer programs, not humans) handle them. Is "memory" implemented into solving programs? It doesn't seem to be in the ones I use, unless of course I've been misusing them.

Isnt "chain memory" usually called "net"?

Not as employed here : using existing placements within a single chain is different from having branching chains which either merge or converge.
A net after all is multiple strands (hence the name) : here we are in the same strand.

[Pat]

Isnt "chain memory" usually called "net"?

yes, exactly.

a stream of implications
where each step stands on its own (no "memory")
is used in "chains"

as soon as we need "memory",
i.e. a step uses results from some earlier step,
this is called a "net"