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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Mon Jun 30, 2008 11:39 am Post subject: Very Hard + |
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Since today's VH wasn't, here is an extra puzzle for you. | Code: | Puzzle: M4109527sh(15)
+-------+-------+-------+
| . 2 . | . . . | . 6 . |
| . 3 . | . 6 4 | . 5 . |
| . 5 6 | . 7 . | 3 4 . |
+-------+-------+-------+
| 5 . . | . 2 1 | . . 4 |
| 6 . . | 5 . 7 | . . 1 |
| . . . | 8 9 . | . . . |
+-------+-------+-------+
| . 9 7 | . 3 . | 4 1 . |
| . 6 . | . 8 5 | . 9 . |
| . 4 . | . . . | . 2 . |
+-------+-------+-------+ |
The Menneske rating still has me baffled. Usually I can solve this level with one or two advanced moves. This one took more.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Jun 30, 2008 4:46 pm Post subject: |
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1) After basics, there was an almost Type 6 UR with a strong link on each candidate, making two eliminations
2) W-Wing
3) XY-Chain |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Mon Jun 30, 2008 6:30 pm Post subject: |
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| Code: | +-------------------------------------+
| 1479 2 148 | 139 5 38 | 18 6 789 |
| 179 3 18 | 129 6 4 | 128 5 2789 |
| 19 5 6 | 129 7 28 | 3 4 289 |
----------------------------------------
| 5 7 39 | 36 2 1 | 69 8 4 |
| 6 8 29 | 5 4 7 | 29 3 1 |
| 234 1 234 | 8 9 36 | 5 7 26 |
---------------------------------------
| 8 9 7 | 26 3 26 | 4 1 5 |
| 12 6 12 | 4 8 5 | 7 9 3 |
| 3 4 5 | 7 1 9 | 68 2 68 |
+-------------------------------------+ |
Following Marty, I looked for a UR. One is in r12c37.
| Code: | +--------------------------------------+
| 1479 2 18+4 | 139 5 38 | 18+ 6 789 |
| 179 3 18+ | 129 6 4 | 18+2 5 2789 |
| 19 5 6 | 129 7 28 | 3 4 289 |
----------------------------------------
| 5 7 39 | 36 2 1 | 69 8 4 |
| 6 8 29 | 5 4 7 | 29 3 1 |
| 24 1 234 | 8 9 36 | 5 7 26 |
----------------------------------------
| 8 9 7 | 26 3 26 | 4 1 5 |
| 12 6 12 | 4 8 5 | 7 9 3 |
| 3 4 5 | 7 1 9 | 68 2 68 |
+--------------------------------------+ |
As the two cells in the left-hand corners are conjugate with respect to 8, 8 may be eliminated from r3c7. Equally, those in the right-hand corners are conjugate with respect to 1 so this is eliminated from r1c3.
| Code: | +---------------------------------------+
| 179+4 2 48 | 19+3 5 38 | 18 6 79+8 |
| 179+ 3 18 | 129+ 6 4 | 12 5 279+8 |
| 19+ 5 6 | 129+ 7 28 | 3 4 29+8 |
-----------------------------------------
| 5 7 39 | 36 2 1 | 69 8 4 |
| 6 8 29 | 5 4 7 | 29 3 1 |
| 24 1 234 | 8 9 36 | 5 7 26 |
-----------------------------------------
| 8 9 7 | 26 3 26 | 4 1 5 |
| 12 6 12 | 4 8 5 | 7 9 3 |
| 3 4 5 | 7 1 9 | 68 2 68 |
+---------------------------------------+ |
There is now a (1279) MUG in r123c149. If c9b3 contains 8, r1c7 must be 1. The only other possibility is that r1c14 contains 3 or 4. In this case a (348) locked set is formed with r1c36 and again r1c7 is 1. Placing 1 here solves the puzzle.
I’m beginning to wonder if MUGs are rather more common than first thought. Perhaps it is a matter of looking for them.
Steve |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Mon Jun 30, 2008 7:35 pm Post subject: |
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Marty: What is an ALMOST Type 6 UR? Sounds like almost pregnant?
I found a Type 4 UR with a diagonal variant.
Couldn't get no further. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Jun 30, 2008 9:04 pm Post subject: |
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I, too, used that 18 UR, though in a different way: exploiting the 4=2 induced strong link. The grid (without the <3> in r6c1 as shown by Steve):
| Code: | +---------------+------------+--------------+
| 1-479 2 a148 | 139 5 38 | 18 6 789 |
| 179 3 18 | 129 6 4 |b128 5 c2789 |
| 19 5 6 | 129 7 28 | 3 4 c289 |
+---------------+------------+--------------+
| 5 7 39 | 36 2 1 | 69 8 4 |
| 6 8 29 | 5 4 7 | 29 3 1 |
|e24 1 23-4 | 8 9 36 | 5 7 d26 |
+---------------+------------+--------------+
| 8 9 7 | 26 3 26 | 4 1 5 |
| 12 6 12 | 4 8 5 | 7 9 3 |
| 3 4 5 | 7 1 9 | 68 2 68 |
+---------------+------------+--------------+ |
The UR strong link, ab, is followed by the c9 grouped strong link, cd, and the bivalue strong link, e, to eliminate <4>s as shown. Or,
UR[(4)r1c3=(2)r2c7] - (2)r23c9=(2)r6c9 - (2=4)r6c1; r1c1|r6c3<>4
After that, a 6-cell XY-Chain finished things off. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Jun 30, 2008 9:13 pm Post subject: |
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| By the way, basic Medusa starting on <3>s leads to a Medusa Wrap in <8> and solves the puzzle in "one" step. It's always interesting to find a Medusa Wrap, I think. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Jun 30, 2008 9:14 pm Post subject: |
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| Quote: | | Marty: What is an ALMOST Type 6 UR? Sounds like almost pregnant? |
Craig, a Type 6 is with the bivalue cells on the diagonals and with one of the candidates being an X-Wing. When that occurs, each bivalue cell is solved with that X-Wing number.
The 18 cells in boxes 1 and 3 are diagonal, but there's no X-Wing, so I call it an "almost" Type 6 because the pattern is there. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Jun 30, 2008 9:45 pm Post subject: |
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| Asellus wrote: | | By the way, basic Medusa starting on <3>s leads to a Medusa Wrap in <8> and solves the puzzle in "one" step. It's always interesting to find a Medusa Wrap, I think. |
I found a chain by Medusa coloring on <368>. Here it is: | Code: | +-------------+-------------+-------------+
| 79 2 4 | 139 5 3r8g | 18g 6 789 |
| 179 3 8 | 19 6 4 | 12 5 27 |
| 19 5 6 | 129 7 28 | 3 4 89 |
+-------------+-------------+-------------+
| 5 7 39 | 36 2 1 | 69 8 4 |
| 6 8 29 | 5 4 7 | 29 3 1 |
| 4 1 23 | 8 9 3g6r | 5 7 26g |
+-------------+-------------+-------------+
| 8 9 7 | 26 3 26 | 4 1 5 |
| 2 6 1 | 4 8 5 | 7 9 3 |
| 3 4 5 | 7 1 9 |6g8r 2 6r8 |
+-------------+-------------+-------------+ |
Starting in R1C6, the chain is in C6, R6, C9, R9, and C7, resulting in two <8g> in R1. r (red) must be true.
This is one chain I picked out of the Medusa net. Others are possible.
Keith |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Mon Jun 30, 2008 10:11 pm Post subject: |
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Marty: Lost you there mate because I used the diagaonal variant of a Type 4 UR.
| Code: |
+-------+------+-------+
| . .148| . . .|18 . . |
| . . 18| . . .|128. . |
+-------+-------+------+
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Thus - unless I am wrong - there are only two 1's in C7 so we can remove the 1 from <148>
And there are only two 8's in C3 ao we can remove 8 from <128>
------------------
Is that your type 6 UR?
I recently discussed this with Keith.
I still can't understand why a Type 5 UR is simply a minor diagonal variation of a Type 2 UR. Whereas the diagonal variant of the Type 4 UR is still a Type 4 - despite the fact that its resolution is radically different. You could of course argue that all all UR's have the same undelying logic. In which case - why bother with any Types.
Edited note: Sorry Marty - your post appeared after I posted mine.
I will read and digest. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Jun 30, 2008 10:43 pm Post subject: |
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| cgordon wrote: | Marty: Lost you there mate because I used the diagaonal variant of a Type 4 UR.
| Code: |
+-------+------+-------+
| . .148| . . .|18 . . |
| . . 18| . . .|128. . |
+-------+-------+------+
|
Thus - unless I am wrong - there are only two 1's in C7 so we can remove the 1 from <148>
And there are only two 8's in C3 ao we can remove 8 from <128>
------------------
Is that your type 6 UR?
I recently discussed this with Keith.
I still can't understand why a Type 5 UR is simply a minor diagonal variation of a Type 2 UR. Whereas the diagonal variant of the Type 4 UR is still a Type 4 - despite the fact that its resolution is radically different. You could of course argue that all all UR's have the same undelying logic. In which case - why bother with any Types.
Sorry for the rant. |
Craig,
Why don't you take a look at the classifications on Sudopedia,
http://www.sudopedia.org/wiki/Uniqueness_Test
and also those that are on Ruud's Sudocue (nightmare) site,
http://www.sudocue.net/guide.php#UR
Maybe we should rewrite the classifications!
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Jul 01, 2008 5:32 am Post subject: |
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| Code: | .------------------.------------------.------------------.
| 1479 2 148 | 139 5 38 | 18 6 789 |
| 179 3 18 | 129 6 4 | 128 5 2789 |
| 19 5 6 | 129 7 28 | 3 4 289 |
:------------------+------------------+------------------:
| 5 7 39 | 36 2 1 | 69 8 4 |
| 6 8 29 | 5 4 7 | 29 3 1 |
| 24 1 234 | 8 9 36 | 5 7 26 |
:------------------+------------------+------------------:
| 8 9 7 | 26 3 26 | 4 1 5 |
| 12 6 12 | 4 8 5 | 7 9 3 |
| 3 4 5 | 7 1 9 | 68 2 68 |
'------------------'------------------'------------------' |
we have had the URs and MUGs... how about a strictly chain method??
starting with this w-wing with extended pincers...
visually...
in notation...(2=6)r7c4-(6)r7c6=(6)r6c6-(6=2)r6c9-(2)r5c7=(2)r2c7; r2c4<>2
leads too...
| Code: | .------------------.------------------.------------------.
| 1479 2 148 | 139 5 38 | 18 6 789 |
| 179 3 18 | 19 6 4 | 128 5 2789 |
| 19 5 6 | 129 7 28 | 3 4 89 |
:------------------+------------------+------------------:
| 5 7 39 | 36 2 1 | 69 8 4 |
| 6 8 29 | 5 4 7 | 29 3 1 |
| 24 1 234 | 8 9 36 | 5 7 26 |
:------------------+------------------+------------------:
| 8 9 7 | 26 3 26 | 4 1 5 |
| 12 6 12 | 4 8 5 | 7 9 3 |
| 3 4 5 | 7 1 9 | 68 2 68 |
'------------------'------------------'------------------' |
xy-wing{1,8,9} removes 8 from r2c79 (ehem... 3 cell xy-chain)
xy-wing{1,8,9} removes 1 from r1c13" "
leads too...
| Code: | .---------------.---------------.---------------.
| 79 2 4 | 139 5 #38 |#18 6 789 |
| 179 3 8 | 19 6 4 |#12 5 -279 |
| 19 5 6 | 129 7 28 | 3 4 89 |
:---------------+---------------+---------------:
| 5 7 39 | 36 2 1 | 69 8 4 |
| 6 8 29 | 5 4 7 | 29 3 1 |
| 4 1 23 | 8 9 #36 | 5 7 #26 |
:---------------+---------------+---------------:
| 8 9 7 | 26 3 26 | 4 1 5 |
| 2 6 1 | 4 8 5 | 7 9 3 |
| 3 4 5 | 7 1 9 | 68 2 68 |
'---------------'---------------'---------------' |
the marked xy-chain eliminates the 2 from r2c9
{26}-{36}-{38}-{18}-{12}...done. |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Tue Jul 01, 2008 6:36 pm Post subject: |
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Keith: I looked at the first of those references for UR's and am confused by the first example for Type 6 - since there appear to be strong links on all the rows and columns.
But regardless of this - is my assumption above correct? That is: are we OK with a diagonal Type 4 UR where there are only 2 of the UR pair candidates in a row or column.
Meanwhile, it looks like a Type 6 UR is (as Marty noted) a diagonal variant of a Type 4.
I would have come up with a more rational classification - but I have decided not to change it. 
Seems amazing how many times the Type 4's or 6's crop up. |
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