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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Wed Aug 04, 2010 12:28 am Post subject: Another Menneske |
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I enjoyed this one. | Code: | Puzzle: M588257sh(0)
+-------+-------+-------+
| 7 . . | 9 . . | . . 4 |
| . . 2 | . . . | 1 . . |
| . 8 6 | . . 1 | 3 9 . |
+-------+-------+-------+
| . . . | . . 6 | 5 . . |
| . 3 . | 4 . 5 | . 2 . |
| . . 1 | 8 . . | . . . |
+-------+-------+-------+
| . 5 3 | . . 8 | 6 7 . |
| . . 4 | . . . | 8 . . |
| 1 . . | 2 . . | . . 5 |
+-------+-------+-------+ |
Menneske's puzzle ratings are one Scandinavian thing I do not understand (another is the music of ABBA).
I believe the ratings are not based on solving the puzzle. Rather, they reflect some heuristic based on counting back doors, strong links, ...
Anyway, if you like puzzles that are kind of hard, but unpredictable, go to Menneske and ask for a Super Hard. Often, the result will be a Very Hard(0), like this one.
The only puzzles that have a non-zero numerical rating are the Super Hards. I usually do not bother with a ranking above 30.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Aug 04, 2010 1:48 am Post subject: |
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| Not very elegant. Implications of 29 UR eliminated a couple of 6s. Then XY-Wing (279) followed by XY-Chain; r8c9, r9c5<>3. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Aug 04, 2010 1:59 am Post subject: |
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Perhaps, more elegant: The implications of a 79 DP on the 2nd Floor put 6 in R9C5. Before the end of basics: | Code: | +----------------+----------------+----------------+
| 7 1 5 | 9 68 3 | 2 68 4 |
| 3 9 2 | 67 678 4 | 1 5 68 |
| 4 8 6 | 5 2 1 | 3 9 7 |
+----------------+----------------+----------------+
| 28 24 79 | 37 379 6 | 5 1348 139 |
| 68 3 79 | 4 1 5 | 79 2 68 |
| 5 46 1 | 8 379 2 | 479 346 39 |
+----------------+----------------+----------------+
| 29 5 3 | 1 4 8 | 6 7 29 |
| 269 267 4 | 36 5 79 | 8 13 1239 |
| 1 67 8 | 2 36 79 | 49 34 5 |
+----------------+----------------+----------------+ |
Keith |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Wed Aug 04, 2010 7:19 am Post subject: |
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An m-wing with pincer transport..
| Code: | | m-wing(36) (6=3)r9c5 - r9c8=(3-6)r6c8=r5c9 - r5c1=r8c1 ; r8c4<>6, r8c2<>6 |
Keith, there are many confusing things about Scandinavia! If you are ever offered the chance to eat Sorstromming, pass! Fish that has gone so rotten in the can that it expands with the gasses...  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Aug 04, 2010 4:25 pm Post subject: |
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Not elegant, but my solver found an atypical alternative for the M-Wing.
| Code: | after basics and Swordfish on <6>
+-----------------------------------------------------+
| 7 1 5 | 9 68 3 | 2 68 4 |
| 3 9 2 | 67 78 4 | 1 5 68 |
| 4 8 6 | 5 2 1 | 3 9 7 |
|-----------------+-----------------+-----------------|
| 28 24 79 | 37 379 6 | 5 48 1 |
| 68 3 79 | 4 1 5 | 79 2 68 |
| 5 46 1 | 8 79 2 | 479 346 39 |
|-----------------+-----------------+-----------------|
| 29 5 3 | 1 4 8 | 6 7 29 |
| 269 27 4 | 36 5 79 | 8 1 239 |
| 1 67 8 | 2 36 79 | 49 34 5 |
+-----------------------------------------------------+
# 37 eliminations remain
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| Code: | Yes, also present after basics.
M-Wing Type 1A (6=3)r9c5 - r9c8 = (3-6)r6c8 = (6)r1c8 => r1c5<>6 -or-
M-Wing Type 1B (6=3)r9c5 - r9c8 = (3-6)r6c8 = (6)r6c2 => r9c2<>6
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-or- Multi-Value Colors (present after Swordfish)
| Code: | limited Pink/Amber coloring on <3> limited Blue/Green coloring on <6>
+-----------------------------------+ +-----------------------------------+
| . . . | . . 3 | . . . | | . . . | . B6 . | . G6 . |
| 3 . . | . . . | . . . | | . . . | 6 . . | . . 6 |
| . . . | . . . | 3 . . | | . . 6 | . . . | . . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . . | 3 3 . | . . . | | . . . | . . 6 | . . . |
| . 3 . | . . . | . . . | | 6 . . | . . . | . . 6 |
| . . . | . . . | . P3 3 | | . 6 . | . . . | . B6 . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . 3 | . . . | . . . | | . . . | . . . | 6 . . |
| . . . | 3 . . | . . 3 | | 6 . . | 6 . . | . . . |
| . . . | . P3 . | . A3 . | | . 6 . | . G6 . | . . . |
+-----------------------------------+ +-----------------------------------+
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Notice that r6c8=P3+B6 and r9c5=P3+G6. If Pink is true, then both alternatives for <6> fail.
Conclusion: <3> can be eliminated in Pink cells. |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Wed Aug 04, 2010 4:45 pm Post subject: |
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| Danny, never seen that colouring method before - is it generally a fruitful technique or one for when all else fails? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Aug 04, 2010 4:52 pm Post subject: |
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| peterj wrote: | | Danny, never seen that colouring method before - is it generally a fruitful technique or one for when all else fails? |
Hello Peter,
I'm not certain how often it's fruitful because my solver only finds it through Templates ... and that's just before it searches for chains.
I posted a very difficult puzzle where this technique was the final step. This is the second puzzle posted by Keith where this technique was present as a final step. I believe Keith's other puzzle was a Menneske as well.
Regards, Danny |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Wed Aug 04, 2010 5:42 pm Post subject: |
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I found another of my almost als - xz and can make the same one step elimination via this vacker sak:
ANP(34=6)r69c8-(6=8)r1c8-(8=6)r1c5-(6=3)r9c5-(3=4)r9c8; r4c8<>4
Ed - Nice puzzle thanks Keith. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Aug 04, 2010 7:56 pm Post subject: |
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Addendum for Peter:
If you check, you'll see that the candidates for <3> and <6> each form a full coloring cycle; i.e., only two possible choices for each. My grids above only depicts a portion of each cycle present in the conflict.
I restrict my Templates() routine to only search for Multi-Value Colors conflicts where the two values conform to this cyclic constraint. Thus, my solver is only reporting a small fraction of the Multi-Value Colors conflicts that may exist in a puzzle. I have a more extensive search disabled for Multi-Value Colors because it's extremely unlikely that anyone would try using that logic.
Finally, since everything is based on strong links on two different values, it's probably easier to find an equivalent chain.
Regards, Danny |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Wed Aug 04, 2010 8:23 pm Post subject: |
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| Are there other names for this technique Danny ? I've seen Marty refer to something called Medusa(?)when he's tackling a really tough puzzle. Is this similar ? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Aug 04, 2010 10:18 pm Post subject: |
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| Mogulmeister wrote: | | Are there other names for this technique Danny ? I've seen Marty refer to something called Medusa(?)when he's tackling a really tough puzzle. Is this similar ? |
Mogulmeister, there probably are other names with which I'm not familiar -- including 3D Medusa. To tell the truth, I just used what came to mind in describing what I was doing. _  _
Regards, Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Aug 05, 2010 3:39 am Post subject: |
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| peterj wrote: | An m-wing with pincer transport..
| Code: | | m-wing(36) (6=3)r9c5 - r9c8=(3-6)r6c8=r5c9 - r5c1=r8c1 ; r8c4<>6, r8c2<>6 |
Keith, there are many confusing things about Scandinavia! If you are ever offered the chance to eat Sorstromming, pass! Fish that has gone so rotten in the can that it expands with the gasses... |
Peter,
One of the reasons I got an education and saved for a decent retirement is that I would not have to consider offal etc. as a delicacy. Surstromming is an acquired taste I plan never to acquire.
en.wikipedia.org/wiki/Surströmming
So far as fish is concerned, my tastes extend only to anchovies on my pizza, and to a South African delicacy called "harders", which are dried, salted fish. Young herrings, I believe. Fish jerky.
Similarly, in my first college summer job in South Africa I worked in a gold mine. Two miles underground. The greatest incentive you can ever have to get an education that ensures a cubicle job!
Mogulmeister,
I will look for current examples of Medusa coloring. It is a really cool, if somewhat extreme, technique. Your basic M-wing is the simplest example, though I think the M-wing generalizations we now mostly use are not cases of Medusa coloring.
Best wishes,
Keith |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Aug 05, 2010 8:56 am Post subject: |
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I appreciate it Keith. I know it is a technique Marty has mentioned but I assumed, possibly wrongly, that it was labour intensive and required several sheets of paper or somesuch so I never investigated. I've seen someone mention "medusa wrap" as well - I assume they're related ?
PS Whilst I may agree with you about the rotten Swedish fish, I think many of you in the US are missing out. Eating offal can be a really vacker sak. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Aug 05, 2010 10:35 pm Post subject: Medusa Coloring |
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MM,
Medusa coloring (colouring) is not labor (labour) intensive. It is not complicated either. Here is the basic idea:
If you have a two-candidate cell, XY, either X is true or Y is true (and vice-versa). That is a strong link.
If a candidate X occurs only twice in any row, column or block, then it is true in one cell or the other. That is a strong link.
Medusa puts these together. Let's look at a simple M-wing:
a and b are any set of candidates. = is a strong link. X and Y are particular candidates.
Start from the left. Color the first X green, the second red, etc. You have
| Code: | XY = aX = XY = bY
r g r |
Either r(ed) or g(reen) is true. Now, note that in the first and third cells, Y must be g(reen). And then, in the last cell, Y must be r(ed).
| Code: | XY = aX = XY = bY
rg g rg r |
The first and last cells are pincers in Y.
So, the recipe is simple: Pick a bivalue cell. Color the strong links in one candidate to other cells. Then, color to other candidates in bivalue cells. Repeat until your net cannot be expanded, then examine the net for implications.
Look here
http://www.sudocue.net/guide.php#Medusa
and here:
http://www.sudopedia.org/wiki/3D_Medusa
I have an unproven theory that any BUG+1 will succumb to Medusa. That would be a good place to start practicing.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Aug 06, 2010 12:11 am Post subject: |
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Alert: Keith's M-Wing Medusa scenario does not work for gM-Wing !!!
| Code: | gM-Wing: (2=5)r9c1 - r9c6 = (5-2)r2c6 = (2)r5c6 => r5c1<>2
+--------------------------------------------------------------+
| 6 28 5 | 48 9 3 | 27 1 478 |
| 4 1 7 | 58 6 c25 | 23 9 38 |
| 3 28 9 | 1 248 7 | 26 5 468 |
|--------------------+--------------------+--------------------|
| 9 3 16 | 4678 478 146 | 167 2 5 |
| 1-2 5 8 | 367 237 d126 | 9 4 367 |
| 7 4 126 | 356 235 9 | 136 8 36 |
|--------------------+--------------------+--------------------|
| 15 7 13 | 2 35 8 | 4 6 9 |
| 8 9 34 | 3467 1 46 | 5 37 2 |
| a25 6 234 | 9 @3457 b45 | 8 37 1 |
+--------------------------------------------------------------+
# 60 eliminations remain
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The presence of <5> as a candidate in r9c5 blocks the strong link coloring that Keith's M-Wing scenario relies upon.
| Code: | gM-Wing solution space
*----------------------------------*
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| M-Wing solution space |
| *-----------------------* |
| | | |
| | | |
| | | |
| *-----------------------* |
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*----------------------------------*
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Aug 06, 2010 4:13 am Post subject: |
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| daj95376 wrote: | Alert: Keith's M-Wing Medusa scenario does not work for gM-Wing !!!
| Code: | gM-Wing: (2=5)r9c1 - r9c6 = (5-2)r2c6 = (2)r5c6 => r5c1<>2
+--------------------------------------------------------------+
| 6 28 5 | 48 9 3 | 27 1 478 |
| 4 1 7 | 58 6 c25 | 23 9 38 |
| 3 28 9 | 1 248 7 | 26 5 468 |
|--------------------+--------------------+--------------------|
| 9 3 16 | 4678 478 146 | 167 2 5 |
| 1-2 5 8 | 367 237 d126 | 9 4 367 |
| 7 4 126 | 356 235 9 | 136 8 36 |
|--------------------+--------------------+--------------------|
| 15 7 13 | 2 35 8 | 4 6 9 |
| 8 9 34 | 3467 1 46 | 5 37 2 |
| a25 6 234 | 9 @3457 b45 | 8 37 1 |
+--------------------------------------------------------------+
# 60 eliminations remain
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The presence of <5> as a candidate in r9c5 blocks the strong link coloring that Keith's M-Wing scenario relies upon.
| Code: | gM-Wing solution space
*----------------------------------*
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| M-Wing solution space |
| *-----------------------* |
| | | |
| | | |
| | | |
| *-----------------------* |
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*----------------------------------*
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Danny,
We are in violent agreement!
I conceived (identified?), and christened (named?), the basic M-wing as the simplest case of an elimination that can be made by Medusa coloring.
ronk in particular, and Nataraj before him, and others, have generalized the idea of an M-wing. The eliminations made by these generalizations will almost always (I believe) not be found by Medusa coloring.
Yes, the terminology is a little messy. But, we make up the terminology as we go along. We do not have the luxury of establishing all the theory, and then defining a consistent terminology.
Keith |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Fri Aug 06, 2010 7:44 am Post subject: |
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All much appreciated.
Not sure if I will conciously need/use the technique but glad to know about it. Mind you, I said the same thing to myself (a long time ago) about ERs when I first read Havard on the subject and now I use them regularly. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Fri Aug 06, 2010 10:35 am Post subject: |
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| keith wrote: | | ronk in particular, and Nataraj before him, and others, have generalized the idea of an M-wing. The eliminations made by these generalizations will almost always (I believe) not be found by Medusa coloring. |
If one excludes Medusa Bridge and Medusa Complex from Medusa Coloring, that is correct. However, the description at Ruud's site implies inclusion. That said, I don't know if Medusa coloring includes grouping of single-digt candidates. |
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