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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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 Posted: Sat Jun 21, 2008 11:59 am Post subject: June 21 DB |
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The June 21 DB is stubborn. First a skyscraper in <2>, then an xy-chain with pincers again of <2>.
Earl
| Code: |
+-------+-------+-------+
| . . . | . . 5 | . 2 3 |
| 7 . . | . 1 . | . 9 . |
| . 6 . | . . 7 | 1 . . |
+-------+-------+-------+
| . 8 . | 7 3 . | . . 1 |
| . . 1 | . . . | 3 . . |
| 3 . . | . 5 9 | . 7 . |
+-------+-------+-------+
| . . 2 | 6 . . | . 1 . |
| . 3 . | . 4 . | . . 7 |
| 6 1 . | 9 . . | . . . |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Jun 21, 2008 3:31 pm Post subject: |
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No need for the skyscraper, really. Since we're going to use an xy-chain eventually, why not right away?
24 (r4c6) and 29 (r5c9) as pincers, connected via 45-56-69 in row 4.
| Code: |
+--------------------------+--------------------------+--------------------------+
| 1 9 48 | 48 6 5 | 7 2 3 |
| 7 245 3458 | 2348 1 248 | 45 9 6 |
| 245 6 345 | 234 9 7 | 1 8 45 |
+--------------------------+--------------------------+--------------------------+
| 259 8 56# | 7 3 24* | 69# 45# 1 |
| 259 7 1 | 248 28 6 | 3 45 29* |
| 3 24 46 | 1 5 9 | 68 7 28 |
+--------------------------+--------------------------+--------------------------+
| 45 45 2 | 6 7 3 | 89 1 89 |
| 8 3 9 | 5 4 1 | 2 6 7 |
| 6 1 7 | 9 28 28 | 45 3 45 |
+--------------------------+--------------------------+--------------------------+
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edit 1932 GMT+2: "since we're going to use an xy-chain..."
Last edited by nataraj on Sat Jun 21, 2008 5:34 pm; edited 1 time in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jun 21, 2008 3:38 pm Post subject: |
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Here's what I came up with.
After Earl's skyscraper: | Code: |
+----------------+----------------+----------------+
| 1 9 48 | 48 6 5 | 7 2 3 |
| 7 245 3458 | 23 1 48 | 45 9 6 |
| 245 6 345 | 23 9 7 | 1 8 45 |
+----------------+----------------+----------------+
| 259 8 56 | 7 3 24 | 69 45 1 |
| 259 7 1 | 48 28 6 | 3 45 29 |
| 3 24 46 | 1 5 9 | 68 7 28 |
+----------------+----------------+----------------+
| 45 45 2 | 6 7 3 | 89 1 89 |
| 8 3 9 | 5 4 1 | 2 6 7 |
| 6 1 7 | 9 28 28 | 45 3 45 |
+----------------+----------------+----------------+ |
Medusa multicoloring takes out <4> in R2C2. (Start on the <2>'s in R5C59. The pincer cells are R1C3 and R6C2.)
This reveals an extended XY-wing [25 - 24 - 46, 56] that takes out <5> in R2C3, and the puzzle is solved.
Keith |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Sat Jun 21, 2008 8:56 pm Post subject: |
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| Since I am very anti-chain I had to plod away at this one. A UR on 28 didn't seem to do much - nor an ER on <2>. But perhaps they eventually were of use because after the <248> xy wing and another ER on <4> (using R1/B5) I was able to finish. Though I struggled spotting the triples. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Jun 21, 2008 9:01 pm Post subject: |
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| A UR, ER, coloring, multi-coloring and an XY-Wing chain weren't enough for me to crack it, so I was down to Medusa or XY-Chain. I XY-Chained it, killing two birds with one stone, both finishing the puzzle and verbing another technique. |
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cathyv
Joined: 25 Apr 2008
Posts: 7
Location: Danbury, CT
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| Posted: Mon Jun 23, 2008 2:41 pm Post subject: |
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I have a question about XY-chains. I understand how they work when someone else points them out to me, but I have trouble finding them on my own. Are there any tricks or secrets about where or when to start looking for them?
Thanks, Cathy |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Mon Jun 23, 2008 3:22 pm Post subject: |
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| cathyv wrote: | Are there any tricks or secrets about where or when to start looking for them?
Thanks, Cathy |
Cathy, I am afraid not. "when?" seems to be easier to answer, I tend to say: when lesser means fail. But then again I often find xy-chains while looking for xy-wings / w-wings (both are special cases of xy-chains, so maybe there is no big difference after all).
Many times, a good starting point is a useless xy-wing. Other nice starting points are repeated sequences of the same pair. I the grid I posted (above) I would look at the 45-45-45 and 28-28-28 chains. Such patterns are useful because the 28-28-28 works like a single cell 28 (the end cells are either both 2 or both 8 ). If we can find two cells to tack on to either end we have something quite like an xy-wing. Unfortunately, no such luck here (but see footnote below)
There is a failed xy-wing, though: 46-56-45 (col 3 and row 4). It does not eliminate anything, but we know that either r6c3 or r4c8 is 4 (maybe even both). But if r4c8=4 then r4c6=2. And if r6c3=4 then r6c2=2. This new xy-chain still doesn't much. But if r6c2=2 then r6c9=8 then r5c9=2. Now this xy-chain (connecting r4c6 and rc9) is really useful. We can remove 2 from r5c45. The chain is still rather long. Sometimes it is possible to shorten the chain. Let's see what we can do. We already know exactly what to look for: connect the 4 in r4c6 with the 9 in r5c9. The three cells 45,56 and 69 in row 4 do exactly that.
I don't know a surefire recipe for finding useful xy-chains. Else I'd probably go for them earlier. (Multi-)Coloring, xy-wings and w-wings, on the other hand can be found using simple search patterns.
______________________
BTW, a good example for the first starting point I mentioned (sequences of like cells) is Asellus' post in this thread "6/20-6/22 competition puzzles"
In his first diagram,
| Code: |
+-----------------+-----------------+--------------+
| 7 6 49 | 3459 148 3589 | 1345 2 359 |
| 234-9 23 249 | 6 14 59* | 145 7 8 |
| 1 8 5 | 349 2 7 | 34 6 39 |
+-----------------+-----------------+--------------+
| 25# 17 6 | 25# 9 4 | 8 3 17 |
| 29* 4 279 | 8 3 1 | 6 5 27 |
| 8 125 3 | 7 6 25# | 9 4 12 |
+-----------------+-----------------+--------------+
| 35 35 78 | 1 78 6 | 2 9 4 |
| 6 27 1 | 2349 47 239 | 357 8 35 |
| 24 9 2478 | 23 5 238 | 37 1 6 |
+-----------------+-----------------+--------------+
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you can see the sequence 25-25-25 in boxes 4 and 5. Together with 29 in r5c1 and 59 in r2c6 we get a very useful xy-chain that removes 9 from r2c1, which makes r5c1=9. |
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