| View previous topic :: View next topic |
| Author |
Message |
daj95376
Joined: 23 Aug 2008
Posts: 3854
|
 Posted: Thu Dec 18, 2008 6:27 pm Post subject: Set G Puzzle 58 |
 |
|
| 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 |
|
| Back to top |
|
 |
storm_norm
Joined: 18 Oct 2007
Posts: 1741
|
| Posted: Thu Dec 18, 2008 9:25 pm Post subject: |
|
|
| 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 |
|
|
| Back to top |
|
|
tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
|
| Posted: Fri Dec 19, 2008 5:51 am Post subject: |
|
|
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 |
|
| Back to top |
|
|
daj95376
Joined: 23 Aug 2008
Posts: 3854
|
| Posted: Fri Dec 19, 2008 6:19 am Post subject: |
|
|
| 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 |
*-----------------------------------------------------------------------------*
|
|
|
| Back to top |
|
|
tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
|
| Posted: Fri Dec 19, 2008 2:04 pm Post subject: |
|
|
| 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.  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 |
|
| Back to top |
|
|
Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
|
| Posted: Fri Dec 19, 2008 4:21 pm Post subject: |
|
|
| 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. |
|
| Back to top |
|
|
tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
|
| Posted: Fri Dec 19, 2008 10:51 pm Post subject: |
|
|
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........ 
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 |
|
| Back to top |
|
|
daj95376
Joined: 23 Aug 2008
Posts: 3854
|
| Posted: Fri Dec 19, 2008 11:24 pm Post subject: |
|
|
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 |
*-----------------------------------------------------------------------------*
|
|
|
| Back to top |
|
|
Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
|
|
| Back to top |
|
|
tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
|
| Posted: Sat Dec 20, 2008 5:22 am Post subject: |
|
|
| 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 |
|
| Back to top |
|
|
storm_norm
Joined: 18 Oct 2007
Posts: 1741
|
| Posted: Sat Dec 20, 2008 7:13 am Post subject: |
|
|
| 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. 
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?  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. 
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 |
|
| Back to top |
|
|
daj95376
Joined: 23 Aug 2008
Posts: 3854
|
| Posted: Sat Dec 20, 2008 12:45 pm Post subject: |
|
|
| 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.
Last edited by daj95376 on Sat Dec 20, 2008 1:25 pm; edited 1 time in total |
|
| Back to top |
|
|
tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
|
| Posted: Sat Dec 20, 2008 1:19 pm Post subject: |
|
|
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. 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 |
|
| Back to top |
|
|
storm_norm
Joined: 18 Oct 2007
Posts: 1741
|
| Posted: Sat Dec 20, 2008 11:16 pm Post subject: |
|
|
Ted,
ask Danny for a cipher. 
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. |
|
| Back to top |
|
|
daj95376
Joined: 23 Aug 2008
Posts: 3854
|
| Posted: Sat Dec 20, 2008 11:58 pm Post subject: |
|
|
| 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
|
|
|
| Back to top |
|
|
storm_norm
Joined: 18 Oct 2007
Posts: 1741
|
| Posted: Sun Dec 21, 2008 1:06 am Post subject: |
|
|
| 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. |
|
| Back to top |
|
|
daj95376
Joined: 23 Aug 2008
Posts: 3854
|
| Posted: Sun Dec 21, 2008 6:13 pm Post subject: |
|
|
| 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. |
|
| Back to top |
|
|
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
