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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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