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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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 Posted: Sat Sep 20, 2008 12:57 pm Post subject: Sept 20 DB |
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The September 20 DB is no one-trick pony. I had to color three times, then an xy-wing. Any quick solutions out there?
Earl
| Code: |
+-------+-------+-------+
| . . 1 | . 4 8 | . . 6 |
| . 3 4 | . . . | . . 1 |
| 8 . . | . . 9 | . 4 . |
+-------+-------+-------+
| 1 . . | . 5 6 | 2 . . |
| . . . | . . . | . . . |
| . . 2 | 9 8 . | . . 5 |
+-------+-------+-------+
| . 5 . | 7 . . | . . 9 |
| 6 . . | . . . | 5 3 . |
| 3 . . | 6 9 . | 1 . . |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Sep 20, 2008 2:38 pm Post subject: |
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At this point | Code: | +-------------------+-------------------+-------------------+
| 2579 279 1 | 235 4 8 | 379 2579 6 |
| 2579 3 4 | 25 6 27 | 8 2579 1 |
| 8 267 56 | 1235 137 9 | 37 4 23 |
+-------------------+-------------------+-------------------+
| 1 79 3 | 4 5 6 | 2 79 8 |
|-4579 8 56 | 123 137 1237 | 34679 1679 34B |
| 47 467A 2 | 9 8 137 |3-467 167 5 |
+-------------------+-------------------+-------------------+
| 24 5 8 | 7 13 13 | 46 26 9 |
| 6 1 9 | 8 2 4 | 5 3 7 |
| 3 24a 7 | 6 9 5 | 1 8 24b |
+-------------------+-------------------+-------------------+ |
a skyscraper (coloring) on <4> takes out the candidates shown. (Any cell that sees bot A and B cannot be <4>.)
Then, all I can see is a chain that takes out <7> in R6C7, leading to an XY-wing.
Not very pretty.
Keith |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Sep 20, 2008 2:40 pm Post subject: |
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Nice puzzle Earl.
I used kites instead of coloring plus the xy-wing to finish it off; very similar to your solution.
Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Sep 20, 2008 4:21 pm Post subject: |
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| I used coloring on 4, three ERs and an XY-Wing on 364 with pincer coloring finished it off. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Sep 20, 2008 5:16 pm Post subject: |
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This is better. After the skyscraper we have: | Code: | +-------------------+-------------------+-------------------+
| 2579 27-9 1 | 235 4 8 | 379# 2579# 6 |
| 2579 3 4 | 25 6 27 | 8 2579# 1 |
| 8 267 56 | 1235 137 9 | 37 4 23 |
+-------------------+-------------------+-------------------+
| 1 79@ 3 | 4 5 6 | 2 79@ 8 |
| 579 8 56 | 123 137 1237 | 34679 1679 34 |
| 47 467 2 | 9 8 137 | 367 167 5 |
+-------------------+-------------------+-------------------+
| 24 5 8 | 7 13 13 | 46 26 9 |
| 6 1 9 | 8 2 4 | 5 3 7 |
| 3 24 7 | 6 9 5 | 1 8 24 |
+-------------------+-------------------+-------------------+ |
There is an ER in Box 3, with the strong link in R4, eliminating <9> from R1C2. Leading to the 346 XY-wing which I find solves it without pincer coloring.
Somehow I had the idea that ER eliminations would always be found by other patterns such as kites and skyscrapers. That does not seem to be true here.
Keith
Last edited by keith on Sat Sep 20, 2008 8:27 pm; 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: Sat Sep 20, 2008 6:45 pm Post subject: |
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| keith wrote: | Somehow I had the idea that ER eliminations would always be found by other patterns such as kites and skyscrapers. That does not seem to be true here.
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Could you say all kites and skyscrapers are er's but not all er's are kites and skyscrapers?
Nice find in a good puzzle!  |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Sat Sep 20, 2008 7:00 pm Post subject: |
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| keith wrote: | Somehow I had the idea that ER eliminations would always be found by other patterns such as kites and skyscrapers. That does not seem to be true here.
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| Code: | +-------------------+-------------------+-------------------+
| 2579 27-9 1 | 235 4 8 |*379 2579 6 |
| 2579 3 4 | 25 6 27 | 8 2579 1 |
| 8 267 56 | 1235 137 9 | 37 4 23 |
+-------------------+-------------------+-------------------+
| 1 *79 3 | 4 5 6 | 2 *79 8 |
| 579 8 56 | 123 137 1237 |*34679 1679 34 |
| 47 467 2 | 9 8 137 | 367 167 5 |
+-------------------+-------------------+-------------------+
| 24 5 8 | 7 13 13 | 46 26 9 |
| 6 1 9 | 8 2 4 | 5 3 7 |
| 3 24 7 | 6 9 5 | 1 8 24 |
+-------------------+-------------------+-------------------+ |
Looking at it closer, isn't this a kite? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Sep 20, 2008 7:21 pm Post subject: |
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| Quote: | | Looking at it closer, isn't this a kite? |
Yes!  But are the kite and the ER somehow "the same"? R5C7 is irrelevant in the ER logic.
Keith |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Sat Sep 20, 2008 7:37 pm Post subject: |
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[quote="keith"][quote]Looking at it closer, isn't this a kite?[/quote]
Yes! But are the kite and the ER somehow "the same"? R5C7 is irrelevant in the ER logic.
[/quote]
Yes irrelevant to one er, but doesn't it form another "mostly overlapping" er? One with and one without a corresponding kite or skyscraper. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Sep 20, 2008 8:07 pm Post subject: |
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It is also a Skyscraper in r24.
I have so far found one ER elimination for which I was unable to find an alternate elimination. Unfortunately, I didn't keep any notes so cannot retrieve it. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Sep 20, 2008 8:55 pm Post subject: |
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| Asellus wrote: | | It is also a Skyscraper in r24. |
Man!!
I only started looking for an ER when others had mentioned using them in this puzzle, and I was unable to solve it without a chain. Can't see the wood for the trees!
Let me point out the chain: | Code: | +-------------------+-------------------+-------------------+
| 2579 279 1 | 235 4 8 | 379 2579 6 |
| 2579 3 4 | 25 6 27 | 8 2579 1 |
| 8 267 56 | 1235 137 9 | 37f 4 23e |
+-------------------+-------------------+-------------------+
| 1 79 3 | 4 5 6 | 2 79 8 |
| 579 8 56 | 123 137 1237 | 34679 1679 34 |
| 47a 467 2 | 9 8 137 | 36-7 167 5 |
+-------------------+-------------------+-------------------+
| 24b 5 8 | 7 13 13 | 46 26 9 |
| 6 1 9 | 8 2 4 | 5 3 7 |
| 3 24c 7 | 6 9 5 | 1 8 24d |
+-------------------+-------------------+-------------------+ |
You can easily argue that if a is not <7> then f must be <7>, and vice-versa. Sort of a transported, extended XY-wing:
47 - 24 - 24 -24 -23 - 37
collapses (with the transport on 24) to
47 - 24 - 23 - 37
collapses (with the pseudo-cell in R3) to
47 - 24 - 27.
I thought, Aha! Medusa coloring should find this. But no, not that I could see.
Asellus can probably explain why the chain is bi-directional if you argue that either pincer is not <7>. But, if you start with the proposition that either one of them is <7>, you go nowhere. The conclusion, I believe, is that one or both of the pincers are <7>. Just like an XY-wing.
Keith
Last edited by keith on Sat Sep 20, 2008 10:09 pm; edited 2 times in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Sep 20, 2008 9:16 pm Post subject: |
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| Quote: | | Leading to the 346 XY-wing which I find solves it without pincer coloring. |
I do believe that comment is for my benefit. You referenced the expression, "Can't see the forest for the trees." That makes two of us. The direct elimination of the 4 in r9c9 is so obvious that I didn't see it and used coloring in order to zap it. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Sep 20, 2008 10:06 pm Post subject: |
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| Quote: | | I do believe that comment is for my benefit. |
Marty, yes, and no. I have no idea what your grid looked like, or even if it is the same wing. (I had no intention of implying that you may have missed something. How could I? My fallibility is documented in excruciating detail above!)
You said "with coloring", which caused me to note mine was "without".
Best wishes,
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Sep 21, 2008 3:07 am Post subject: |
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| Skyscraper in 4, either one of two Skyscrapers in 9, and XY-Wing. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Sep 21, 2008 5:47 am Post subject: |
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| keith wrote: | | The conclusion, I believe, is that one or both of the pincers are <7>. Just like an XY-wing. |
That is correct: the pincer digits have a strong inference link (via the chain). The chain, by the way, is just your garden variety XY-Chain. In a way, we don't really need the name XY-Wing since it is just a 3-cell XY-Chain, the more universal term. (But I'm not advocating that... just to be clear.)
I don't have the antipathy to XY Chains that many have expressed in this forum. For me, they certainly aren't just random guesswork. I look for likely possible pincers. Candidates that have few remaining instances are not reasonable choices for pincer digits. And, there is no point in starting an XY-Chain search with a digit that isn't found in any other bivalue in the grid, for instance. So, I look for a digit that has is a candidate all over the place and which is present in several bivalues. That makes it much more likely to be a pincer of an XY-Chain. Also, let's say that <4>s meet this criterion and I see a 49 bivalue. But, if there are no other bivalues containing <9>, then that bivalue is a waste of time for an XY Chain. By reasoning like this, the search for XY-Chains can be reduced to a sensible (in my opinion) process and not just lucky guesswork.
In the puzzle above, there are lots of unsolved <7>s. And, there are 5 bivalues containing <7>. So, looking for an XY-Chain with <7> pincers is a reasonable thing to do.
You might like to note that your chain can be extended via the conjugate <7>s in b2 to eliminate <7> from r2c1. While usually called "transporting the pincer," it is just an extension of the chain using that strong (conjugate) link. In other words, "transporting" is a euphemism for using an AIC (for folks who don't like to admit to such).
| Quote: | | I thought, Aha! Medusa coloring should find this. But no, not that I could see. |
That's because the XY-Chain has weak links along the way and basic Medusa doesn't color weak links. However, if you did Medusa multi-coloring, you would eventually happen across this elimination (provided that other eliminations you might find first hadn't destroyed it). But then, this puzzle isn't one where the resort to Medusa multi-coloring would be reasonable since less involved approaches present themselves. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Sep 21, 2008 6:10 am Post subject: |
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Just for good measure:
That XY-Chain can also be extended on the other end via the two 79 bivalues in r4. This eliminates <7>s from r12c8 and from r5c7. So that's a lot of <7> eliminations due to XY Chains. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Sep 21, 2008 7:52 am Post subject: |
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| Either Skyscraper in 9 => [r4c2]=9 => [r4c8]=7 => total of seven eliminations in 7 (plus eliminations in 9) |
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sudocraz
Joined: 28 Apr 2008
Posts: 53
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| Posted: Sun Sep 21, 2008 11:48 pm Post subject: |
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Phew!
I was just about to try and post this very puzzle, when I saw it already here.
No wonder I couldn't solve it! Way over my head. I am just beginning, with the help of some members of this board, to learn the xy wings. I will keep this puzzle and see if I can solve it someday in the future.
My husband solved it as he always does when he can't solve it logically. He made an educated guess. It works like a charm when you guess.  |
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