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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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 Posted: Sun May 09, 2010 11:30 am Post subject: May 9 DB (MM 1764) |
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No useful VH steps here afaics ...
| Code: | +-------+-------+-------+
| . 6 . | . . . | . 3 . |
| 8 9 . | 6 3 . | . . 5 |
| . . 5 | . . . | . . 4 |
+-------+-------+-------+
| 4 . . | . . 5 | . 8 . |
| . . . | . 8 4 | . . . |
| . 8 . | 3 . . | . . 7 |
+-------+-------+-------+
| 1 . . | . . . | 6 . . |
| 7 . . | . 1 2 | . 4 8 |
| . 5 . | . . . | . 2 . |
+-------+-------+-------+ |
One possible solution
| Quote: | w-wing(17) pincer transport
(1=7)r2c6-r2c8=r7c8-(7=1)r9c7 -r9c9=r1c9; r1c6<>1, r2c8<>1 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun May 09, 2010 1:06 pm Post subject: |
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After a previous puzzle where Peter and I discussed X-Colors, I had a nagging feeling about X-Colors as described in Sudopedia because I knew there were times when I had gotten into trouble applying X-Colors as they described. As luck would have it, I ran across an example in this puzzle.
| Code: | after basics
+--------------------------------------------------------------+
| 2 6 17 | 45 45 1789 | 1789 3 19 |
| 8 9 4 | 6 3 17 | 2 17 5 |
| 3 17 5 | 2 79 1789 | 1789 6 4 |
|--------------------+--------------------+--------------------|
| 4 127 1379 | 179 679 5 | 139 8 26 |
| 56 127 1379 | 179 8 4 | 1359 159 26 |
| 56 8 19 | 3 2 69 | 4 159 7 |
|--------------------+--------------------+--------------------|
| 1 4 2 | 8 579 379 | 6 579 39 |
| 7 3 6 | 59 1 2 | 59 4 8 |
| 9 5 8 | 47 467 367 | 17 2 13 |
+--------------------------------------------------------------+
# 67 eliminations remain
+-----------------------------------+
| . . . | 5 5 . | . . . |
| . . . | . . . | . . 5 |
| . . 5 | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . 5 | . . . |
| 5 . . | . . . | 5 5 . |
| 5 . . | . . . | . 5 . |
|-----------+-----------+-----------|
| . . . | . 5 . | . 5 . |
| . . . | 5 . . | 5 . . |
| . 5 . | . . . | . . . |
+-----------------------------------+
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I start Blue/Green coloring in row 1 and proceed until I can't color anymore.
| Code: | +-----------------------------------+
| . . . | B G . | . . . |
| . . . | . . . | . . 5 |
| . . 5 | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . 5 | . . . |
| 5 . . | . . . | G 5 . |
| 5 . . | . . . | . 5 . |
|-----------+-----------+-----------|
| . . . | . B . | . G . |
| . . . | G . . | B . . |
| . 5 . | . . . | . . . |
+-----------------------------------+
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| step (3.1) from Sudopedia wrote: | If all but one and only one cell (called the Exception Cell) of all the candidates in a house are peers of cells colored with the same color (let's say color A), then this Exception cell can be colored with the SAME COLOR (A).
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Now, cell r6c8 in [r6] is a peer of two Green cells (and no Blue cells). So I take step (3.1) to imply that r6c1 is an Exception Cell and that it can be colored Green. If I do this, then I've made a mistake because r6c1=5 is true and Green=5 is false.
BTW: W-Wing (7=1)r2c8 - r1c9 = r9c9 - (1=7)r9c7 => r13c7,r7c8<>7.
[Edit: removed reference to my X-Colors approach being different.]
Last edited by daj95376 on Sun May 09, 2010 6:30 pm; edited 1 time in total |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sun May 09, 2010 2:15 pm Post subject: |
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| daj95376 wrote: | | Code: | +-----------------------------------+
| . . . | B G . | . . . |
| . . . | . . . | . . 5 |
| . . 5 | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . 5 | . . . |
| 5 . . | . . . | G 5 . |
| 5 . . | . . . | . 5 . |
|-----------+-----------+-----------|
| . . . | . B . | . G . |
| . . . | G . . | B . . |
| . 5 . | . . . | . . . |
+-----------------------------------+
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| step (3.1) from Sudopedia wrote: | If all but one and only one cell (called the Exception Cell) of all the candidates in a house are peers of cells colored with the same color (let's say color A), then this Exception cell can be colored with the SAME COLOR (A).
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Now, cell r6c8 in [r6] is a peer of two Green cells (and no Blue cells). So I take step (3.1) to imply that r6c1 is an Exception Cell and that it can be colored Green. If I do this, then I've made a mistake because r6c1=5 is true and Green=5 is false. |
Why do you think coloring r6c1 Green indicates either true or false for r6c1=5? |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Sun May 09, 2010 2:30 pm Post subject: |
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Danny, first off I agree with you about x-colours as a (not) useful technique in the armory!
However, my understanding is that the technique does not claim that the two coloured sets are conjugates of each other, nor that all elements in the set are neccessarily all true or false. All it claims is that one of sets, B and G, is all true - the other may be all false or indeed have true elements in it (as in this case). The technique focusses on trying to find which of B and G cannot be all true and therefore that the other one must be all true. This is reflected in steps 4.2/4.3 setting the other set true - the subsequent discussion in the plain text is somewhat more confused however!
I always think of step 3.1 as 'if this was the set that is all-true than this cell will also be true and part of that set'.
My penny's worth - but again, I stress, I agree it's not a technique to be recommended! |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun May 09, 2010 6:35 pm Post subject: |
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| ronk wrote: | | Why do you think coloring r6c1 Green indicates either true or false for r6c1=5? |
Sorry. I should have been more specific about using the results from solving the puzzle to show the contradiction of assigning Green to cell r6c1. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun May 09, 2010 6:45 pm Post subject: |
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[Withdrawn: X-Colors is more involved than I originally thought.]
Last edited by daj95376 on Mon May 10, 2010 4:11 am; edited 1 time in total |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Sun May 09, 2010 6:46 pm Post subject: |
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Would this be an extended m-wing?
| Code: | *-----------------------------------------------------------*
| 2 6 17 | 45 45 1789 | 1789 3 19 |
| 8 9 4 | 6 3 17 | 2 17 5 |
| 3 17 5 | 2 79 1789 | 1789 6 4 |
|-------------------+-------------------+-------------------|
| 4 127 1379 | 179 679 5 | 139 8 26 |
| 56 127 1379 | 179 8 4 | 1359 159 26 |
| 56 8 19 | 3 2 69 | 4 159 7 |
|-------------------+-------------------+-------------------|
| 1 4 2 | 8 579 379 | 6 579 39 |
| 7 3 6 | 59 1 2 | 59 4 8 |
| 9 5 8 | 47 467 367 | 17 2 13 |
*-----------------------------------------------------------*
(1)r1c9=r9c9-(1=7)r9c7-r7c8=(7-1)r2c8=(1)r2c6; r1c6,r2c8<>1 stte |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun May 09, 2010 7:31 pm Post subject: |
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| arkietech wrote: | Would this be an extended m-wing?
| Code: | *-----------------------------------------------------------*
| 2 6 17 | 45 45 1789 | 1789 3 19 |
| 8 9 4 | 6 3 17 | 2 17 5 |
| 3 17 5 | 2 79 1789 | 1789 6 4 |
|-------------------+-------------------+-------------------|
| 4 127 1379 | 179 679 5 | 139 8 26 |
| 56 127 1379 | 179 8 4 | 1359 159 26 |
| 56 8 19 | 3 2 69 | 4 159 7 |
|-------------------+-------------------+-------------------|
| 1 4 2 | 8 579 379 | 6 579 39 |
| 7 3 6 | 59 1 2 | 59 4 8 |
| 9 5 8 | 47 467 367 | 17 2 13 |
*-----------------------------------------------------------*
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(1)r1c9=r9c9-(1=7)r9c7-r7c8=(7-1)r2c8=(1)r2c6; r1c6,r2c8<>1 stte |
I don't think so because your strong/weak inferences in blue are opposite of an M-Wing.
With a little editing of the notation, I see an extended/transported W-Wing.
(1)r1c9=r9c9-(1=7)r9c7-r7c8=r2c8-(7=1)r2c6; r1c6,r2c8<>1 |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun May 09, 2010 7:58 pm Post subject: |
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Choose your poison: | Code: | +----------------+----------------+----------------+
| 2 6 17 | 45 45 1789 | 1789 3 19f |
| 8 9 4 | 6 3 17a | 2 17b 5 |
| 3 17 5 | 2 79 1789 | 1789 6 4 |
+----------------+----------------+----------------+
| 4 127 1379 | 179 679 5 | 139 8 26 |
| 56 127 1379 | 179 8 4 | 1359 159 26 |
| 56 8 19 | 3 2 69 | 4 159 7 |
+----------------+----------------+----------------+
| 1 4 2 | 8 579 379 | 6 579c 39 |
| 7 3 6 | 59 1 2 | 59 4 8 |
| 9 5 8 | 47 467 367 | 17d 2 13e |
+----------------+----------------+----------------+ |
M-wing: b and d have the same value, so a and d are an M-wing with pincers 1. Extend the pincer d via e to f. a and f are pincers on 1.
W-Wing: a and d are a W-wing with pincers 1. Strong link bc on 7. Extend as above.
"Extended" means slightly different things to different people.
There is more.
a) With the strong link on 1 in C9 ef, bd are a W-wing with pincers 7.
b) ad are a remote pair (taking out 7 in R9C6).
If you think about it, all the above can only be true if b and d are both 7.
Keith |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sun May 09, 2010 8:22 pm Post subject: |
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ALS Two Sets:
(in orange) X {1,9} in r1c9
(in green) Z {1,3,5,7,9} which is all the squares in b9 except r9c7 
Restricted common is 7 at r27c8 and common candidate is 1 removed at r1c9 solving the puzzle.
Which works in a similar area to Peter but with different technique and elimination.
Last edited by Mogulmeister on Mon May 10, 2010 6:23 am; edited 2 times in total |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Sun May 09, 2010 8:42 pm Post subject: |
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| Quote: | | Okay, then we disagree on what is meant by coloring. |
I am not trying to defend x-colouring - just telling you what my understanding is! The colouring I use - like everybody else- is straight colouring of conjugate links. I guess x-colouring is more a process than a pattern. It does not exhibit the same conjugate property as normal colouring.
Keith was right - shouldn't go there.
Nobody seems to use it anyway! |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun May 09, 2010 10:04 pm Post subject: |
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| Quote: | | Keith was right - shouldn't go there. |
Actually, what I meant to say is that I was not using X-coloring, and I did not want to be drawn into a discussion about it.
From the little I know, X-coloring seems to be a recipe (algorithm) and prone to errors or misinterpretations. But, I really don't know enough to say.
I use (grouped) coloring a lot, particularly when looking for generalized M-wings. You have to be very careful! In simple coloring, if A implies B, then B implies A. With grouped coloring, if A implies B, B does not generally imply A.
Then, there is grouped multicoloring, which can get quite hairy! I do not have any recipes or method classifications. I argue the logic (very carefully) for each case.
Best wishes,
Keith |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Mon May 10, 2010 2:20 am Post subject: DB |
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There is a W-wing (17) based on strong pairs of one's in C9 that solves the puzzle in one step.
Earl |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon May 10, 2010 3:25 am Post subject: |
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ANP(59)r7c8|r8c7 = (7)r7c8 - (7=1)r2c8 - (1=9)r1c9; r7c9<>9
Ted |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Mon May 10, 2010 3:41 am Post subject: |
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| daj95376 wrote: | After coloring r6c1=G and r5c1=B, we now have Blue+Green cells in [r5] that indicate r5c8<>5.
| Code: | +-----------------------------------+
| . . . | B G . | . . . |
| . . . | . . . | . . 5 |
| . . 5 | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . 5 | . . . |
| B . . | . . . | G 5 . |
| G . . | . . . | . 5 . |
|-----------+-----------+-----------|
| . . . | . B . | . G . |
| . . . | G . . | B . . |
| . 5 . | . . . | . . . |
+-----------------------------------+
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After coloring the entire conjugate chain, coloring r6c1 Green is a valid application of "step 3.1." However, no other cells can then be colored Blue. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon May 10, 2010 4:09 am Post subject: |
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| ronk wrote: | | After coloring the entire conjugate chain, coloring r6c1 Green is a valid application of "step 3.1." However, no other cells can then be colored Blue. |
Yes, I discovered that mistake when I went to the Programmers Forum and reread the description there of X-Colors. I was on my way to correct my above post when I saw your reply.
I now believe that there is more going on in X-Colors than I wish to resolve. I'm going to drop it as a technique of interest.
Regards, Danny |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon May 10, 2010 6:10 am Post subject: |
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| peterj wrote: | I am not trying to defend x-colouring - just telling you what my understanding is! The colouring I use - like everybody else- is straight colouring of conjugate links. I guess x-colouring is more a process than a pattern. It does not exhibit the same conjugate property as normal colouring.
Keith was right - shouldn't go there.
Nobody seems to use it anyway! |
Okay, after a lot of review and thinking about X-Colors, I believe that I understand and agree with your position. Here's what appears to be happening.
During the first two steps of X-Coloring, it follows the normal conjugate coloring of cells and each color -- Blue/Green -- represents a partition on the candidate. Only one partition can be true for the candidate.
When step 3.1 is reached, the logic xx over to weak links based on one color. If this color is true for the candidate, then the step 3.1 cells produced by this color are also true. However, if this color turns out to be false for the candidate, then there is no way to tell if the additionally colored cells are true or false.
Since the step 1&2 Green cells turn out to be false for the candidate (in the solution), I can't assume that the step 3.1 Green cells should be false as well. A fallacy on my part ... and probably your and ronk's points that I missed!
Bottom Line: I think everyone agrees that they'd prefer to stay clear of X-Colors.
Last edited by daj95376 on Mon May 10, 2010 6:14 am; edited 2 times in total |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Mon May 10, 2010 6:12 am Post subject: Re: DB |
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| Earl wrote: | There is a W-wing (17) based on strong pairs of one's in C9 that solves the puzzle in one step.
Earl |
I think Earl that Peter already described that one in the first post above. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon May 10, 2010 6:20 am Post subject: |
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| Mogulmeister wrote: | | Earl wrote: | There is a W-wing (17) based on strong pairs of one's in C9 that solves the puzzle in one step.
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Yes Earl, Peter described that one in the first post above. |
Hmmmm. I believe that Peter mentioned a transported W-Wing based on <7> in [c8]. I mentioned the W-Wing based on <1> in [c9]. Earl may have missed it since I used a white font color. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Mon May 10, 2010 6:25 am Post subject: |
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| Did you look at Peter's comment below his post ? He says (17) W wing with pincer transport |
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