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Set G Puzzle 58

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Dec 18, 2008 6:27 pm    Post subject: Set G Puzzle 58 Reply with quote

Code:
 +-----------------------+
 | 2 . . | 8 . . | 6 . . |
 | . 9 . | . 2 . | . . . |
 | . . . | . . . | . 2 . |
 |-------+-------+-------|
 | 8 . . | 2 . . | . 7 . |
 | . 7 . | . 4 . | . . . |
 | . . . | . . 7 | . 4 5 |
 |-------+-------+-------|
 | 6 . . | . . . | 4 3 8 |
 | . . 1 | 3 . 4 | 2 9 . |
 | . . . | . . 8 | 1 . . |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site

[Edit: Dropped initial UR.]


Last edited by daj95376 on Fri Dec 19, 2008 1:34 am; edited 4 times in total
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Thu Dec 18, 2008 9:25 pm    Post subject: Reply with quote

Code:
.------------------------.------------------------.------------------------.
| 2       34      3457   | 8       379     359    | 6       1       349    |
| 1345    9       34567  | 14567   2       1356   | 57      8       34     |
| 1345    1346    8      | 145679  13679   13569  | 57      2       349    |
:------------------------+------------------------+------------------------:
| 8       346     3456   | 2       369     3569   | 39      7       1      |
| 1359    7       35     | 159     4       1359   | 8       6       2      |
| 139     1236    236    | 169     8       7      | 39      4       5      |
:------------------------+------------------------+------------------------:
| 6       5       9      | 17      17      2      | 4       3       8      |
| 7       8       1      | 3       5       4      | 2       9       6      |
| 34      234     234    | 69      69      8      | 1       5       7      |
'------------------------'------------------------'------------------------'

again, its amazing that 7 candidates remain in r3c4.
Quote:
1. x-wing on 5
2. xy-chain... (3=4)r1c2 - (4=6)r4c2 - (6=2)r6c3 - (2=4)r9c3 - (4=3)r9c1; r23c1 <> 3
3. xy-wing (2,4,6)... (2=4)r9c2 - (4=6)r4c2 - (6=2)r6c3; r6c2 and r9c3 <> 2
this next move is changing what a normal W-wing looks like(X=Y) - (Y) = (Y) - (Y=X) extended via X
to...(X=Y) - (Y) = (Y) - (Y=Z) - extended via Z - (Z=X)
X is 5
Y is 9
Z is 6
4. (5=9) r1c6 - (9)r1c5 = (9)r9c5 - (9=6)r9c4 - (6)r6c4 = (6)r6c2 - (6=5)r4c3; r1c3 <> 5
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Fri Dec 19, 2008 5:51 am    Post subject: Reply with quote

I found a potential 6-cell DP but ended up only getting a single deletion as a Type 4 UR.

What I did find were mostly bivalue solutions as follows:
Quote:
x-wing <5>
Type 4 UR <17>
xy-wing <346>
xy-wing <246>
xy-wing <234>
Kite <6> in B4
xyz <169>
w-wing <57>

Did anyone else get deletions from the 6-cell DP?

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Dec 19, 2008 6:19 am    Post subject: Reply with quote

Code:
 After basics, X-Wing <5>, and more basics:  UR Type 4 <17> ???
 *-----------------------------------------------------------------------------*
 | 2       34      457     | 8       379     359     | 6       1       349     |
 | 1345    9       467     | 14567   2       136     | 57      8       34      |
 | 1345    1346    8       | 145679  13679   1369    | 57      2       349     |
 |-------------------------+-------------------------+-------------------------|
 | 8       46      456     | 2       36      356     | 9       7       1       |
 | 159     7       3       | 159     4       19      | 8       6       2       |
 | 19      126     26      | 169     8       7       | 3       4       5       |
 |-------------------------+-------------------------+-------------------------|
 | 6       5       9       | 17      17      2       | 4       3       8       |
 | 7       8       1       | 3       5       4       | 2       9       6       |
 | 34      234     24      | 69      69      8       | 1       5       7       |
 *-----------------------------------------------------------------------------*
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Fri Dec 19, 2008 2:04 pm    Post subject: Reply with quote

daj95376 wrote:
After basics, X-Wing <5>, and more basics: UR Type 4 <17> ???

The potential 6-cell DP I was looking at is: <17> in r7c45, <15> in b2, <57> in r23c7. However in looking at it this morning, it is apparent that b2 does not contain <15> in the appropriate cells. Embarassed Maybe that is why I was not able to get a deletion!

The Type 4 UR I reported is <17> in r37c45 with strong link <1> in c5, thereby deleting <7> from r3c4.

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5126
Location: Rochester, NY, USA

PostPosted: Fri Dec 19, 2008 4:21 pm    Post subject: Reply with quote

Quote:
The Type 4 UR I reported is <17> in r37c45 with strong link <1> in c5, thereby deleting <7> from r3c4.

Ted, a Type 4 is normally understood to be when there is a strong link on one of the candidates in the polyvalue cells, allowing removal of the other candidate from both cells. What you described is what is known as a Hidden UR, or one of the different types of Hidden UR.
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Fri Dec 19, 2008 10:51 pm    Post subject: Reply with quote

Marty, thanks for you comment.

Once again the issue becomes one of terminology! Some time ago I decided I would never use a "Type x" phrase when describing a UR since everything except Types 1 & 2" are not well defined. What do you call a diagonal UR with any strong link, a "Hidden Type 6"? And why "Hidden" instead of another number? Etc, etc........ Confused

Obviously I did not stick to my decision in this case. I have seen references to "Hidden" URs but did not understand exactly what they were. Oh well, in the future I think I will provide gory detail without classification or no comments at all.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Dec 19, 2008 11:24 pm    Post subject: Reply with quote

With the discussion on URs after all, I'm going to include my UR elimination using an approach that is new for me (but not others). It results in additional eliminations -- including Ted's. I have no idea if this approach has a name.

After basics, X-Wing (5), and more basics:

Code:
 UR (57) [r23c47] => [r5c4]=5 or [r7c4]=7   =>  [r3c5]<>1

 [r5c4]=5 [r56c1]=19 [r23c1]<>1 [r3c2]=1    =>  [r3c5]<>1
 [r7c4]=7                       [r7c5]=1    =>  [r3c5]<>1
 *-----------------------------------------------------------------------------*
 | 2       34      457     | 8       379     359     | 6       1       349     |
 | 1345    9       467     | 57+146  2       136     | 57      8       34      |
 | 1345    1346    8       | 57+1469 3679-1  1369    | 57      2       349     |
 |-------------------------+-------------------------+-------------------------|
 | 8       46      456     | 2       36      356     | 9       7       1       |
 | 159     7       3       | 159     4       19      | 8       6       2       |
 | 19      126     26      | 169     8       7       | 3       4       5       |
 |-------------------------+-------------------------+-------------------------|
 | 6       5       9       | 17      17      2       | 4       3       8       |
 | 7       8       1       | 3       5       4       | 2       9       6       |
 | 34      234     24      | 69      69      8       | 1       5       7       |
 *-----------------------------------------------------------------------------*
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Marty R.



Joined: 12 Feb 2006
Posts: 5126
Location: Rochester, NY, USA

PostPosted: Sat Dec 20, 2008 12:58 am    Post subject: Reply with quote

Ted, I think most folks here use the UR Type terminology as described in Keith's primer.

http://www.sudoku.com/boards/viewtopic.php?p=29105#29105
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sat Dec 20, 2008 5:22 am    Post subject: Reply with quote

daj95376 wrote:

After basics, X-Wing (5), and more basics:

Code:
 UR (57) [r23c47] => [r5c4]=5 or [r7c4]=7   =>  [r3c5]<>1

Danny, please help me understand the basic premise. Maybe it is just to late in the day, but the only givens I see is that digit <4> must be in either r2c4 or r3c4. I don't understand why the cell not containing the <4> can't contain any of the other digits <15769>. What forces either [r5c4]=5 or [r7c4]=7?

Ted
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sat Dec 20, 2008 7:13 am    Post subject: Reply with quote

tlanglet wrote:
daj95376 wrote:

After basics, X-Wing (5), and more basics:

Code:
 UR (57) [r23c47] => [r5c4]=5 or [r7c4]=7   =>  [r3c5]<>1

Danny, please help me understand the basic premise. Maybe it is just to late in the day, but the only givens I see is that digit <4> must be in either r2c4 or r3c4. I don't understand why the cell not containing the <4> can't contain any of the other digits <15769>. What forces either [r5c4]=5 or [r7c4]=7?

Ted

Danny's first line, which you copied down is literally what he intends to prove, its like his postulate. Cool

what he is postulating is that if he strips away all the excess "baggage" from r23c4 then he gets the Deadly pattern UR57... as you can see in his grid he puts the excess baggage after the + sign...

and this is very important... a 5 and a 7 can't exist simultaneously in box 2 in column 4. I hope that sinks in, because that is very clever.

why? Question because which ever way you put the 5 or the 7 in the r23c4 cells you end up with two solutions, - deadly, no no.

this reveals some vital information. if you look at column 4, there is only one other 5 and one other 7. so one of them has to be true. Idea

he says, ok, if r5c4 = 5, what happens? if r7c4 = 7, what happens?

then he finds the common consequence of those premises which is that 1 can't live in r3c5.

of course this type of chain usage may lead to some interesting paths through the puzzle, like his naked pair usage in column 1.

sorry for all the edits, but I got my head around it as I was responding.

(1=7)r7c5 - UR57r23c47[(7)r7c4 = (5)r5c4] - ALS[(5)r5c1 = (1)r56c1] - (1)r23c1 = (1)r3c2; r3c5 <> 1
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sat Dec 20, 2008 12:45 pm    Post subject: Reply with quote

tlanglet wrote:
daj95376 wrote:

After basics, X-Wing (5), and more basics:

Code:
 UR (57) [r23c47] => [r5c4]=5 or [r7c4]=7   =>  [r3c5]<>1

Danny, please help me understand the basic premise. Maybe it is just to late in the day, but the only givens I see is that digit <4> must be in either r2c4 or r3c4. I don't understand why the cell not containing the <4> can't contain any of the other digits <15769>. What forces either [r5c4]=5 or [r7c4]=7?

Ted: Norm gave an excellent explanation. Since I'm still new to this approach, I can only provide a slightly different viewpoint.

In order to prevent the <57> UR, having cells [r23c4]=57 must be blocked. Another way of saying this is that at least one other cell that sees [r23c4] must be <5> or <7>; i.e., in [b2] or [c4]. (No, I don't know why other cells/units/houses aren't considered. That's why I'm still stumbling through this approach.)

Now, what originally put me onto considering this approach was that [r5c4]=5 and [r7c4]=7 were the only possibilities in [c4]. Reviewing the (grouped) strong links from these cells showed that they were complements of counterparts in [b2]. Thus, the first half of my UR statement was actually a declaration.

Now, all I needed to show was that these two cells led to a common assignment/elimination. This led to the second half of my UR statement ... and the chains underneath to provide the details.

As for Norm's final Eureka chain, I don't know how to insert UR's into chains, but I have faith that he does.

[Addendum:]

I just now realized why other cells/units/houses aren't considered. If a <5> or <7> was considered in [r23] outside of [b2], then the Naked Pair [r23c7]=57 would force [r23c4]<>5 or [r23c4]<>7. This forces a cell in [b2] or [c4] -- outside of [r23c4] -- to be true for one of these values. Idea


Last edited by daj95376 on Sat Dec 20, 2008 1:25 pm; edited 1 time in total
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sat Dec 20, 2008 1:19 pm    Post subject: Reply with quote

Norm & Danny Thanks for taking the time and energy to respond nicely to my question. As soon as I went to bed last night and relaxed, I fully realized the conditions and implications; the light came on. Idea I sometimes just seem to have a mental block to logical thinking.

In any case, this was a great solution. In some respects it seems similar to the Kraken x-wing in that the implications of conditions "external" to the code pattern are evaluated. Also Danny, I recall that you once employed the same idea of implication analysis when attempting to transport a pincer.

Ted
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sat Dec 20, 2008 11:16 pm    Post subject: Reply with quote

Ted,
ask Danny for a cipher. Laughing
Shocked
Rolling Eyes

ehem, on a more serious note, that UR inference is nice to spot, but is still a shame that only one elimination comes from it. you would think that from a great observation should be more devastation to the puzzle.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sat Dec 20, 2008 11:58 pm    Post subject: Reply with quote

storm_norm wrote:
on a more serious note, that UR inference is nice to spot, but is still a shame that only one elimination comes from it.

What do you mean? Besides the one direct UR elimination, there are four more eliminations that follow from Singles -- including the UR <17> elimination [r3c4]<>7.

Code:
 +--------------------------------------------------------------------------------+
 |  2       34      457     |  8       379     359     |  6       1       349     |
 |  1345    9       467     |  14567   2       136     |  57      8       34      |
 |  1345    1346    8       |  145679  13679   1369    |  57      2       349     |
 |--------------------------+--------------------------+--------------------------|
 |  8       46      456     |  2       36      356     |  9       7       1       |
 |  159     7       3       |  159     4       19      |  8       6       2       |
 |  19      126     26      |  169     8       7       |  3       4       5       |
 |--------------------------+--------------------------+--------------------------|
 |  6       5       9       |  17      17      2       |  4       3       8       |
 |  7       8       1       |  3       5       4       |  2       9       6       |
 |  34      234     24      |  69      69      8       |  1       5       7       |
 +--------------------------------------------------------------------------------+
 # 68 eliminations remain

Code:
 +--------------------------------------------------------------------------------+
 |  2       34      457     |  8       379     359     |  6       1       349     |
 |  1345    9       467     |  1456-7  2       136     |  57      8       34      |
 |  1345    1346    8       |  14569-7 3679-1  1369    |  57      2       349     |
 |--------------------------+--------------------------+--------------------------|
 |  8       46      456     |  2       36      356     |  9       7       1       |
 |  159     7       3       |  159     4       19      |  8       6       2       |
 |  19      126     26      |  169     8       7       |  3       4       5       |
 |--------------------------+--------------------------+--------------------------|
 |  6       5       9       |  7-1     1-7     2       |  4       3       8       |
 |  7       8       1       |  3       5       4       |  2       9       6       |
 |  34      234     24      |  69      69      8       |  1       5       7       |
 +--------------------------------------------------------------------------------+
 # 63 eliminations remain
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storm_norm



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Posts: 1741

PostPosted: Sun Dec 21, 2008 1:06 am    Post subject: Reply with quote

I was simply commenting that the technique itself seems more powerful then the elimination and singles that follow. this technique just has that feel like it should wipe the puzzle out.
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daj95376



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Posts: 3855

PostPosted: Sun Dec 21, 2008 6:13 pm    Post subject: Reply with quote

storm_norm wrote:
I was simply commenting that the technique itself seems more powerful then the elimination and singles that follow. this technique just has that feel like it should wipe the puzzle out.

Ohhhhh!! Yes, I agree. I was disappointed that my effort in tracking down this UR didn't result in a more dramatic reduction of the puzzle.
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