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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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 Posted: Fri Feb 15, 2008 8:52 pm Post subject: Strength of character . . . |
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. . . . (which I haven't got) needed to resist the remote pairs & find some fancy way of doing this straightforward VH standard: M5141532 (44)
| Code: |
+-------+-------+-------+
| 5 3 4 | 8 . . | . 7 . |
| 6 . 1 | . . 7 | . . . |
| . 8 . | . 5 . | . 4 . |
+-------+-------+-------+
| . . 8 | 5 1 . | 4 . . |
| . . . | 9 . 2 | . . . |
| . . . | . 7 4 | . . . |
+-------+-------+-------+
| . . . | . 4 . | . 3 9 |
| 7 . 5 | . . 8 | 6 . 4 |
| . . . | 7 . . | . 8 2 |
+-------+-------+-------+
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Play this puzzle online here |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Feb 15, 2008 10:23 pm Post subject: |
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| Code: |
+-----------------+---------------+-----------------+
| 5 3 4 | 8 269 169 | 129 7 16 |
| 6 29 1 | 4 239 7 | 2389 259 358 |
| 29 8 7 | 1236 5 1369 | 1239 4 136 |
+-----------------+---------------+-----------------+
| 239 67 8 | 5 1 36 | 4 269 37 |
| 134 14567 36 | 9 8 2 | 13 56 1357 |
| 1239 156 2369 | 36 7 4 | 12389 2569 1358 |
+-----------------+---------------+-----------------+
| 8 16 26 | 126 4 5 | 7 3 9 |
| 7 29 5 | 23 239 8 | 6 1 4 |
| 1349 146 369 | 7 69 169 | 5 8 2 |
+-----------------+---------------+-----------------+
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Play this puzzle online at the Daily Sudoku site
I'm just asking, based on some posts I've seen recently. Can you start a chain of the three 29s starting with r8c2, then extend the 2 by saying if r3c1=2, then r6c3=2 and the coloring then allows removal of the 2 from r7c3? |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Fri Feb 15, 2008 11:04 pm Post subject: |
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| Marty wrote: | | I'm just asking, based on some posts I've seen recently. Can you start a chain of the three 29s starting with r8c2, then extend the 2 by saying if r3c1=2, then r6c3=2 and the coloring then allows removal of the 2 from r7c3? |
It would work if the colors/polarities were opposite; but they aren't. It would be grouped coloring, i.e. coloring that exploits a grouped link. I use parentheses to show the colored grouped <2>s:
| Code: |
+---------------------+---------------+-----------------+
| 5 3 4 | 8 269 169 | 129 7 16 |
| 6 2g9 1 | 4 239 7 | 2389 259 358 |
| 2r9 8 7 | 1236 5 1369 | 1239 4 136 |
+---------------------+---------------+-----------------+
| 2(g)39 67 8 | 5 1 36 | 4 269 37 |
| 134 14567 36 | 9 8 2 | 13 56 1357 |
| 12(g)39 156 2r369 | 36 7 4 | 12389 2569 1358 |
+---------------------+---------------+-----------------+
| 8 16 26 | 126 4 5 | 7 3 9 |
| 7 2r9 5 | 23 239 8 | 6 1 4 |
| 1349 146 369 | 7 69 169 | 5 8 2 |
+---------------------+---------------+-----------------+
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Unfortunately, your "pincer" <2>s are both red.
BTW... there is a naked triple in r4 that exposes Victor's remote pairs. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Fri Feb 15, 2008 11:08 pm Post subject: |
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I solved it with an XY Wing, then an ER, then another XY Wing. There were lots of hidden sets and locked candidates along the way!
BTW... that ER almost met my requirements for an "ER-only" elimination. But, the elimination can be accomplished by basic coloring that isn't just a coloring reproduction of the ER. So, it doesn't count. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Feb 16, 2008 1:52 am Post subject: |
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| Quote: | | It would work if the colors/polarities were opposite; but they aren't. |
Oh darn it, but thanks!! It resembles something I saw the other day. I guess I'll have to put more thought into this issue.
P.S. It was Nataraj's pincer extension in this thread that made me ask that. Obviously, pincer extensions are different from coloring.
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2351 |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Feb 16, 2008 7:41 am Post subject: |
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| Marty wrote: | | Obviously, pincer extensions are different from coloring. |
Actually, I believe that pincer extensions can always be seen in terms of coloring. However, it usually involves multi-coloring and grouped coloring concepts. (You can even go multi-digit with Medusa (multi-) coloring if you are brave!) If you are not comfortable with these, then it is best to stick with the simpler ("if this is true then that must be true") "transporting" notions of pincer extension. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Sat Feb 16, 2008 10:34 am Post subject: |
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| Marty, not like you! - you missed a 29 hidden pr in R4 (or 367 naked). This exposes remote 29s which go a long way towards solving the puzzle. I think I needed a W-wing as well. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Feb 16, 2008 3:50 pm Post subject: |
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| Asellus wrote: | | Marty wrote: | | Obviously, pincer extensions are different from coloring. |
Actually, I believe that pincer extensions can always be seen in terms of coloring. However, it usually involves multi-coloring and grouped coloring concepts. (You can even go multi-digit with Medusa (multi-) coloring if you are brave!) If you are not comfortable with these, then it is best to stick with the simpler ("if this is true then that must be true") "transporting" notions of pincer extension. |
I'm not sure what you mean by multi-digit Medusa, but I've gotten into some pretty convoluted Medusas involved with more than one number.
When I said pincer extensions are different from coloring, all I meant was that in pincer extension you're looking for the same polarity and opposite in conventional coloring.
| Quote: | | Marty, not like you! - you missed a 29 hidden pr in R4 (or 367 naked). |
Thanks, but perhaps you overestimate me. But in my defense, I didn't really do this puzzle in my usual pencil-and-paper way. I just quickly did it online until I saw the situation that I asked a question about.  |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Feb 16, 2008 10:01 pm Post subject: |
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| Marty wrote: | | When I said pincer extensions are different from coloring, all I meant was that in pincer extension you're looking for the same polarity and opposite in conventional coloring. |
Well... it depends on how you define your color choices. It is probably best in multi-coloring (which is what pincer extensions are) to use different colors rather than same colors for the "bridge" (here a strong inference bridge rather than a weak inference bridge). The {29} chain coloring above is not a good example because it doesn't actually involve pincers: it is regular ol' basic coloring on <2>.
Usually, pincers have a strong inferential link. One approach is to consider them both "red" and extend the coloring from one (or both) and only consider red-red traps. Better is to color the pincers R-g, then extend one as an RG cluster and the other as an rg cluster, and then look for Rg traps (but ignore rG since they are weakly linked). This is the more usual approach to multi-coloring.
(For more than two clusters, it's best to forget red and green and use Aa, Bb, Cc, etc. clusters.)
| Quote: | | I'm not sure what you mean by multi-digit Medusa |
My point was that folks generally think of pincer extensions limited to a single digit but it doesn't need to be that way. Medusa multi-coloring can exploit the pincer strong inference "bridge" and lead to traps involving other digits.
For instance, two <7> pincers could be colored R-g, with an RG Medusa cluster extended from one and an rg Medusa cluster from the other. Rg combinations trap (but rG combinations do not). Say you found R and g <3>s. You would have converted <7> pincers into <3> pincers.
Bottom line: People usually use weak links to connect clusters in multi-coloring. But strong inferences such as those between wing pincers (or, interestingly, those sometimes found between "extra" digits in a UR) work just as well. It's all a matter of making certain you keep track of which colors/polarities are strongly linked and which are weakly linked. |
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