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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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 Posted: Sun Aug 23, 2009 2:02 am Post subject: Aug 23 VH |
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Old reliable.
Solution: 569 xy-wing
Early Earl |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Aug 23, 2009 3:27 am Post subject: |
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| There is an alternative which not everyone cares for, a Type 2 UR. |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Sun Aug 23, 2009 7:35 am Post subject: |
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I had to use an x-wing on 8s before I could locate and use the xy wing that Earl describes. For me this was a 2-stepper. Did I miss something?
| Code: |
+------------+-----------+-------------+
| 4 2 8 | 6 9 1 | 7 3 5 |
| 39 69 36 | 5 8 7 | 1 4 2 |
| 5 1 7 | 3 4 2 | 8 9 6 |
+------------+-----------+-------------+
| 19 689 56 | 2 167 3 | 59 167 4 |
| 13 7 4 | 9 16 58 | 35 2 18 |
| 2 689 356 | 4 167 58 | 359 167 178 |
+------------+-----------+-------------+
| 6 4 1 | 7 5 9 | 2 8 3 |
| 78 5 2 | 18 3 6 | 4 17 9 |
| 78 3 9 | 18 2 4 | 6 5 17 |
+------------+-----------+-------------+
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Play this puzzle online at the Daily Sudoku site |
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strmckr
Joined: 18 Aug 2009
Posts: 66
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| Posted: Sun Aug 23, 2009 8:23 am Post subject: |
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| Code: | +------------+-----------+-------------+
| 4 2 8 | 6 9 1 | 7 3 5 |
| 39 69 36 | 5 8 7 | 1 4 2 |
| 5 1 7 | 3 4 2 | 8 9 6 |
+------------+-----------+-------------+
| 19 689@ 56 | 2 167 3 | 59 167 4 |
| 13 7 4 | 9 16@ 58 | 35 2 18 |
| 2 689 356 | 4 167 58 | 359 167 178 |
+------------+-----------+-------------+
| 6 4 1 | 7 5 9 | 2 8 3 |
| 78 5 2 | 18 3 6 | 4 17 9 |
| 78 3 9 | 18 2 4 | 6 5 17 |
+------------+-----------+-------------+ |
some hidden singles marked @ |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Sun Aug 23, 2009 3:34 pm Post subject: |
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Ahhh...there are a couple of singles that I did not see. Thanks for pointing them out. Sometimes, I just cannot see those hidden singles even after staring for many minutes at the puzzle.
Of course, the x-wing in boxes 5-6 eliminated the 8 in c2r6, which opened up the 5-6-9 xy wing---and missing those hidden singles proved unnecessary. The flip side is that finding the hidden singles obviated the need for the x-wing.
Thanks for pointing these out, Strmckr.
| strmckr wrote: | | Code: | +------------+-----------+-------------+
| 4 2 8 | 6 9 1 | 7 3 5 |
| 39 69 36 | 5 8 7 | 1 4 2 |
| 5 1 7 | 3 4 2 | 8 9 6 |
+------------+-----------+-------------+
| 19 689@ 56 | 2 167 3 | 59 167 4 |
| 13 7 4 | 9 16@ 58 | 35 2 18 |
| 2 689 356 | 4 167 58 | 359 167 178 |
+------------+-----------+-------------+
| 6 4 1 | 7 5 9 | 2 8 3 |
| 78 5 2 | 18 3 6 | 4 17 9 |
| 78 3 9 | 18 2 4 | 6 5 17 |
+------------+-----------+-------------+ |
some hidden singles marked @ |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sun Aug 23, 2009 9:14 pm Post subject: |
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| Marty R. wrote: | | There is an alternative which not everyone cares for, a Type 2 UR. |
I like type 2 URs  |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Mon Aug 24, 2009 1:56 am Post subject: |
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| Marty R. wrote: | | There is an alternative which not everyone cares for, a Type 2 UR. |
I neither care for nor fail to care for UR IIs.
Could you direct me to where I can find a 'splanation of a UR II ?
Does this involve the 17s in box 5, and 167s in box 6 here?
| Code: |
+-----------+----------+-------------+
| 4 2 8 | 6 9 1 | 7 3 5 |
| 39 69 36 | 5 8 7 | 1 4 2 |
| 5 1 7 | 3 4 2 | 8 9 6 |
+-----------+----------+-------------+
| 19 8 56 | 2 17 3 | 59 167 4 |
| 13 7 4 | 9 6 58 | 35 2 18 |
| 2 69 356 | 4 17 58 | 359 167 178 |
+-----------+----------+-------------+
| 6 4 1 | 7 5 9 | 2 8 3 |
| 78 5 2 | 18 3 6 | 4 17 9 |
| 78 3 9 | 18 2 4 | 6 5 17 |
+-----------+----------+-------------+
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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: Mon Aug 24, 2009 2:43 am Post subject: |
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If you complete the basics, there is not a useful UR in this puzzle:
| Code: | +-------------+-------------+-------------+
| 4 2 8 | 6 9 1 | 7 3 5 |
| 39 69 36 | 5 8 7 | 1 4 2 |
| 5 1 7 | 3 4 2 | 8 9 6 |
+-------------+-------------+-------------+
| 19 8 56 | 2 17 3 | 59 167 4 |
| 13 7 4 | 9 6 58 | 35 2 18 |
| 2 69 356 | 4 17 58 | 359 167 178 |
+-------------+-------------+-------------+
| 6 4 1 | 7 5 9 | 2 8 3 |
| 78 5 2 | 18 3 6 | 4 17 9 |
| 78 3 9 | 18 2 4 | 6 5 17 |
+-------------+-------------+-------------+ |
| Quote: |
Does this involve the 17s in box 5, and 167s in box 6 here? |
Potentially, yes. To break up the deadly pattern, one of R46C8 must be <6>. So, you can eliminate other candidates <6> in B6 or C8. Unfortunately, there aren't any.
If you want info on the various types, here is a good place to start:
http://www.brainbashers.com/sudokuuniquerectangles.asp
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Aug 24, 2009 3:46 am Post subject: |
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| Quote: | | If you complete the basics, there is not a useful UR in this puzzle: |
I suppose it depends on what constitutes "useful." Looking at the implications of each 6 it quickly becomes apparent that r6c2 = 9 either way and that completes the puzzle. If it doesn't immediately eliminate candidates, does that mean it's a Type 3? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Aug 24, 2009 4:03 am Post subject: |
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| Marty R. wrote: | | Quote: | | If you complete the basics, there is not a useful UR in this puzzle: |
I suppose it depends on what constitutes "useful." Looking at the implications of each 6 it quickly becomes apparent that r6c2 = 9 either way and that completes the puzzle. If it doesn't immediately eliminate candidates, does that mean it's a Type 3? |
Marty,
That is a very astute observation! I would say, though, that this is not one of the standard Type 1 through 4 UR eliminations.
Best wishes,
Keith |
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strmckr
Joined: 18 Aug 2009
Posts: 66
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| Posted: Mon Aug 24, 2009 5:10 am Post subject: |
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there isn't any of the rectangles types 1-6
i'll go with
almost unique rectangle.
which uses avoidable sets. 17 in those 4 cells.
acts more kin to a forcing chain over a normal aur but it does the job.
| Code: |
-------------+-------------+-------------+
| 4 2 8 | 6 9 1 | 7 3 5 |
| 39 69 36 | 5 8 7 | 1 4 2 |
| 5 1 7 | 3 4 2 | 8 9 6 |
+-------------+-------------+-------------+
| 19* 8 56* | 2 17@ 3 | 59* 167@ 4 |
| 13 7 4 | 9 6 58 | 35 2 18 |
| 2 69* 356 | 4 17@ 58 | 359 167@ 178|
+-------------+-------------+-------------+
| 6 4 1 | 7 5 9 | 2 8 3 |
| 78 5 2 | 18 3 6 | 4 17 9 |
| 78 3 9 | 18 2 4 | 6 5 17 |
+-------------+-------------+-------------+ |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon Aug 24, 2009 6:09 am Post subject: |
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| I was told by ttt a couple months ago that the existence of the {1,7} cell at r8c8 voids the UR altogether since its in the same house as the roof cells. in this case its in the same column. |
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strmckr
Joined: 18 Aug 2009
Posts: 66
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| Posted: Mon Aug 24, 2009 6:27 am Post subject: |
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how ever the set must be avoided which is why the avoidable set deductions still apply.
the chain of digits only allows the rectangle to void 1 way.
(more of a forcing chain deduction then a real ur...
Last edited by strmckr on Tue Aug 25, 2009 8:00 am; 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: Mon Aug 24, 2009 10:58 pm Post subject: |
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| storm_norm wrote: | | I was told by ttt a couple months ago that the existence of the {1,7} cell at r8c8 voids the UR altogether since its in the same house as the roof cells. in this case its in the same column. |
I understand why one might say that, but I don't quite buy it. The presence of the <17> does not invalidate any UR deductions you may make.
In a sense, it does mean you can make (some?) UR reductions without assuming a uniqueness condition.
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Aug 25, 2009 2:20 am Post subject: |
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| Marty R. wrote: | | Quote: | | If you complete the basics, there is not a useful UR in this puzzle: |
I suppose it depends on what constitutes "useful." Looking at the implications of each 6 it quickly becomes apparent that r6c2 = 9 either way and that completes the puzzle. If it doesn't immediately eliminate candidates, does that mean it's a Type 3? |
the classic type 3 makes eliminations when the non-UR candidates in the roof cells form a locked set with other candidates in the house that the roof cells reside in.
so in a classic type 3 sense. no.
your use of the 6's is just recognizing that neither of the 6's can both be false thus forming a strong link between the two.
UR17[(6)r4c8 = (6)r6c8]
BUT this is the case anyways since the 6's in the UR in column 8 are the only two 6's in column 8. |
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strmckr
Joined: 18 Aug 2009
Posts: 66
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| Posted: Tue Aug 25, 2009 7:57 am Post subject: |
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| Quote: | | In a sense, it does mean you can make (some?) UR reductions without assuming a uniqueness condition. |
an example is the UR 1.1
| Quote: | Definition: an a/b/b/a pattern in a solution grid is anything isomorphic to that shown below:
Code:
. . . | .
a . . | b
b . . | a
---------+---
. . . | .
Fact: if a solution grid (not necessarily unique) contains an a/b/b/a pattern on four unclued cells, C, then C=b/a/a/b is also a solution.
Theorem: if a puzzle-in-progress (that does not necessarily have a unique solution) has pencilmarks as shown below on four unclued cells then the bottom right value resolves to '3':
Code:
. . . | .
1 . . | 2
2 . . | 13
---------+---
. . . | .
Proof: suppose to the contrary the bottom right value resolves to '1'. Then (vacuously) the solution grid contains the 1/2/2/1 pattern on four unclued cells, C. So, by the Fact above, C=2/1/1/2 is also a solution. But wait! - the pencilmarks do not allow that other solution - contradiction. |
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ttt
Joined: 06 Dec 2008
Posts: 42
Location: vietnam
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| Posted: Tue Aug 25, 2009 11:14 am Post subject: |
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Hi All,
| Code: | *--------------*
|.. .|.. .|...|
|.ab.|.abc.|...|
|.ab.|.abd.|...|
|----+-----+---|
|.. .|.ab .|...|
|.. .|.. .|...|
|.. .|.. .|...|
*----+-----+---* |
IMO, in this case I don’t see it as AURs – I see it as avoiding empty cell: at least one of (c, d) must be true
For above case, I see it as bilocation 6’s at col.8
ttt |
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