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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sat Aug 04, 2007 11:11 am Post subject: DB Saturday Puzzle: August 4, 2007 |
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An interesting one ...
| Code: | Puzzle: DB080407 ******
+-------+-------+-------+
| . 1 . | 4 . . | . . 9 |
| 2 4 . | 7 . . | . . 6 |
| 9 . 7 | . . . | . . . |
+-------+-------+-------+
| . . 1 | . . 3 | . 6 . |
| . . . | 2 . 6 | . . . |
| . 3 . | 9 . . | 1 . . |
+-------+-------+-------+
| . . . | . . . | 5 . 2 |
| 5 . . | . . 7 | . 3 8 |
| 1 . . | . . 2 | . 7 . |
+-------+-------+-------+ |
Keith |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Sat Aug 04, 2007 2:54 pm Post subject: |
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Yes, it is. I took ages to spot the trick: perhaps others will do better.
Thanks, Keith.
Steve |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Aug 04, 2007 5:23 pm Post subject: |
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| Quote: | | An interesting one ... |
An understatement perhaps. I'm not sure what Steve's "trick" was, but I worked my butt off on this one.
A couple of URs, simple coloring, X-Wing, Finned X-Wing and a W-Wing. At this point simple coloring finished it off, although there was a BUG+1 pattern which also could've been used. As is frequently the case, I don't know if all my steps were necessary, but when I see a move I play it.
Thanks for posting it. I'm curious to find out if there was a more direct and simple approach than I needed. |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Sat Aug 04, 2007 6:47 pm Post subject: DB Aug 4 |
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Two w-wings were crucial for me:
eliminating the 8's in R7 of box 7, and the 5 in R1C3.
Thanks for the tips.
Earl |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Aug 04, 2007 8:29 pm Post subject: |
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Basic methods get you here:
| Code: | +----------------+----------------+----------------+
| 38 1 56 | 4 36 58 | 7 2 9 |
| 2 4 38 | 7 9 1 | 38 5 6 |
| 9 56 7 | 36 2 58 | 38 4 1 |
+----------------+----------------+----------------+
| 4 9 1 | 58 578 3 | 2 6 57 |
| 78 578 58 | 2 1 6 | 4 9 3 |
| 6 3 2 | 9 57 4 | 1 8 57 |
+----------------+----------------+----------------+
| 378 678 3468 | 368 3468 9 | 5 1 2 |
| 5 2 469 | 1 46 7 | 69 3 8 |
| 1 68 3689 | 3568 3568 2 | 69 7 4 |
+----------------+----------------+----------------+ |
A) There is a Type 1 UR on <57> that solves R4C5 <8>.
B) There is a Type 4 UR on <69> that removes <6> from R89C3.
AND
C) There is a Type 6 UR on <46> that says R7C3 is not <6>. (The UR is also an X-wing on <4>.)
Type 6 UR's that are actually helpful seem to be rather rare. This one (along with the other two UR's) solves the puzzle.
Keith |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Sat Aug 04, 2007 9:01 pm Post subject: |
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I seem to have followed the route used by Earl although I think one w-wing will do.
In the position posted by Keith the two (58) s in r1c6 and r5c3 are linked by the conjugate 8s in box 1. The elimination of 5 from r1c3 brings you home.
Steve |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Sat Aug 04, 2007 9:52 pm Post subject: |
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I found an xy-chain length 4.
Starting with <5> in R5C3 => R1C3=6 => R1C5=3 => R1C1=8, which erases both <8>'s in R2C3 and R5C1, that solves the puzzle |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Sat Aug 04, 2007 10:37 pm Post subject: |
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I lost my grid while posting a reply. So this is the grid after UR 57 in R46 and C59.
| Code: |
+--------------+------------+--------+
|D38 1 B56 | 4 C36 58 | 7 2 9 |
| 2 4 3-8 | 7 9 1 | 38 5 6 |
| 9 56 7 | 36 2 58 | 38 4 1 |
+--------------+------------+--------+
| 4 9 1 | 5 8 3 | 2 6 7 |
| 7-8 578 A58 | 2 1 6 | 4 9 3 |
| 6 3 2 | 9 7 4 | 1 8 5 |
+--------------+------------+--------+
| 378 678 3468 | 368 346 9 | 5 1 2 |
| 5 2 469 | 1 46 7 | 69 3 8 |
| 1 68 3689 | 368 5 2 | 69 7 4 |
+--------------+------------+--------+
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Ruud
Joined: 18 Jan 2006
Posts: 31
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| Posted: Sun Aug 05, 2007 10:26 am Post subject: |
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There is another UR move, but I'm not sure what type it is. It is the UR equivalent of the Broken Wing + Guardians technique.
Here's the grid:
| Code: | +----------------+----------------+----------------+
| 3!8 1 56 | 4 36 58 | 7 2 9 |
| 2 4 38 | 7 9 1 | 38 5 6 |
| 9 56 7 | 36 2 58 | 38 4 1 |
+----------------+----------------+----------------+
| 4 9 1 | 58 578 3 | 2 6 57 |
|*78 *578 58 | 2 1 6 | 4 9 3 |
| 6 3 2 | 9 57 4 | 1 8 57 |
+----------------+----------------+----------------+
|*378 *678 3468 | 368 3468 9 | 5 1 2 |
| 5 2 469 | 1 46 7 | 69 3 8 |
| 1 6!8 3689 | 3568 3568 2 | 69 7 4 |
+----------------+----------------+----------------+ |
There is a possible UR {78} in r57c12. Because digit 7 must occupy 2 spots in the UR, digit 8 must be placed somewhere else in columns 1 or 2. There are only 2 alternatives in these 2 columns. r1c1 and r2c9. At least one of them must contain digit 8, otherwise we would have a deadly pattern. As a result, we can eliminate 8 from r7c1, because it can see both "guardians".
Not much help, but I'm just curious whether this UR logic has been used before.
Ruud |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Sun Aug 05, 2007 12:24 pm Post subject: |
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That�s a nice observation, Ruud!
I have not seen it remarked on before. It is not in Mike Barker�s list of UR types so, if it was known of, it slipped through the net.
As you say, the method is not particularly fruitful here. Next time, who knows �?
Steve |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Aug 05, 2007 1:53 pm Post subject: |
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(There is also a Type 6 reduction: The UR on <78> is also an X-wing on <7>; R7C2 is not <8>.)
I agree this is a nice reduction. You can compare it with something Myth Jellies pointed out:
http://www.sudoku.com/boards/viewtopic.php?t=4204&start=65
This is on the last page (5) of my guide to UR's. There is a discussion following the original post by MJ.
Best wishes,
Keith |
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