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Stuck on a puzzle from the local newspaper.
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jayagee



Joined: 26 Feb 2006
Posts: 7
Location: sunny north dakota

PostPosted: Wed Aug 23, 2006 1:44 am    Post subject: Stuck on a puzzle from the local newspaper. Reply with quote

Puzzle as posted:

XXX XXX 37X
XXX 8X5 94X
XXX 2X7 8X5

4X9 XXX X5X
X5X X8X X3X
X7X XXX 2X4

2X5 3X4 XXX
X43 9X8 XXX
X16 XXX XXX

I got this far:

5XX 1X6 372
X27 835 94X
XXX 2X7 8X5

4X9 72X X58
X52 48X X3X
X7X 65X 2X4

2X5 3X4 XXX
743 9X8 52X
X16 572 4X3

Now Im stuck. I think the answer relates to the 1s at r4, c6 &c7
and at r5, c6 & c7. Doesnt seem like this is a true x-wing since there are 3 1s in r5 and 3 1s in box f or 6. Can someone shed some light???

Thanks!!
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Wed Aug 23, 2006 4:23 am    Post subject: Reply with quote

This is the grid with all candidates filled in based on the position you reached:

Code:
-------------------------------------------------
|5    89   48   |1    49   6    |3    7    2    |
|16   2    7    |8    3    5    |9    4    16   |
|39   36   14   |2    49   7    |8    16   5    |
-------------------------------------------------
|4    36   9    |7    2    13   |16   5    8    |
|16   5    2    |4    8    19   |167  3    79   |
|38   7    18   |6    5    139  |2    19   4    |
-------------------------------------------------
|2    89   5    |3    16   4    |167  1689 79   |
|7    4    3    |9    16   8    |5    2    16   |
|89   1    6    |5    7    2    |4    89   3    |
-------------------------------------------------




Quote:
Now Im stuck. I think the answer relates to the 1s at r4, c6 &c7
and at r5, c6 & c7. Doesnt seem like this is a true x-wing since there are 3 1s in r5 and 3 1s in box f or 6. Can someone shed some light???


That is correct, it is not an X-Wing.

The move that I see involves an XY-Wing, which I don't know if you're familiar with or not. Note the 36 in r4c2, the 16 in r5c1 and the 13 in r4c6. If you experiment with a little chain based in r4c2, you will see that either r4c6 or r5c1 must be "1." Regardless of which it is, r5c6 cannot be "1", therefore that cell is solved with "9" and that breaks the puzzle wide open.

If you are not familiar with the XY-Wing, here is an explanation:

http://www.brainbashers.com/sudokuxywing.asp
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Wed Aug 23, 2006 12:21 pm    Post subject: Reply with quote

I got to this point, which differs from the posted one in that the (1,6) pairs in box 2 and column 4 aren't resolved yet. How did you do that?

Code:

 *-----------------------------------------------------------*
 | 5     89    48    | 16    49    16    | 3     7     2     |
 | 16    2     7     | 8     3     5     | 9     4     16    |
 | 39    36    14    | 2     49    7     | 8     16    5     |
 |-------------------+-------------------+-------------------|
 | 4     36    9     | 7     2     136   | 16    5     8     |
 | 16    5     2     | 4     8     169   | 167   3     79    |
 | 38    7     18    | 16    5     1369  | 2     169   4     |
 |-------------------+-------------------+-------------------|
 | 2     89    5     | 3     16    4     | 167   1689  79    |
 | 7     4     3     | 9     16    8     | 5     2     16    |
 | 89    1     6     | 5     7     2     | 4     89    3     |
 *-----------------------------------------------------------*
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Wed Aug 23, 2006 2:58 pm    Post subject: Reply with quote

I also arrived at the same point as Tracey and have the same question.
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Wed Aug 23, 2006 3:47 pm    Post subject: Reply with quote

I have a question.

If you look at R7C28 and R9C18, it looks something similar to a unique rectangle. Can you therefore assume that cell at R7C8 has to be either a 1 or a 6 ?? The solution will certainly fall out from this assumption, but of course I may be using false logic.
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Wed Aug 23, 2006 3:48 pm    Post subject: Reply with quote

This is the puzzle we talked about over the weekend

http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=1325

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Wed Aug 23, 2006 3:54 pm    Post subject: Reply with quote

Quote:
I got to this point, which differs from the posted one in that the (1,6) pairs in box 2 and column 4 aren't resolved yet. How did you do that?


Tracy, I just wrote onto a blank grid, not the original published puzzle, but the position (s)he had already reached, and proceeded from there. Maybe I should have started with the published puzzle, but I just wanted to see if I could help at the exact point at which (s)he was stuck.

The original poster had already resolved the 16 in box 2 and column 4.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Wed Aug 23, 2006 10:37 pm    Post subject: Reply with quote

Marty,

That's what I thought you did, but I tried to solve it from the beginning and got stuck at the point indicated.

Keith,

Thanks for pointing that out, I didn't realize they were the same. I solved that one shortly after you posted it, but when I tried to recreate what I did I got stopped at this same point. I know the first time I used an XY-wing that excluded the 9 from r5c9 (I think it was (1, 6 & 9) with r6c4 as the stem cell. But that means that r6c8 needs to lose the 1 and I can't figure out how I did that). Has Sudoku finally made me lose my mind?
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Wed Aug 23, 2006 11:23 pm    Post subject: A mind to lose? Reply with quote

Tracy,

I saw your note about an XY-wing, I could not find it but did not comment.

I spent hours staring at the 1's and 6's. I was hoping you would come through with a multicoloring solution that I could not see!

Keith
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jayagee



Joined: 26 Feb 2006
Posts: 7
Location: sunny north dakota

PostPosted: Thu Aug 24, 2006 1:28 am    Post subject: Reply with quote

To Tracy and David. There is an x-wing of 1's at r3,c3 & c8 and r6, c3 & c8. This eliminates 1 at r6,c4 and makes r1,c4 a 1 and of course a 6 at r1 c6.. Those were my last two numbers before being stumped.
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jayagee



Joined: 26 Feb 2006
Posts: 7
Location: sunny north dakota

PostPosted: Thu Aug 24, 2006 1:38 am    Post subject: Reply with quote

To Marty R. Thanks; I 'm not very good with the x-y thing.. I might have noticed it if the 16 in r5,c1 had been in c2, but then again maybe not. that logic is a bit beyond my experience level. Just an old geezer trying to keep up with the young generation.. Thanks again; I,ll file this one away for future reference.
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Thu Aug 24, 2006 1:55 am    Post subject: Reply with quote

Quote:
Just an old geezer trying to keep up with the young generation..


You're not alone. Not only am I an old geezer, I've been one for a number of years. Crying or Very sad
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Aug 24, 2006 2:07 am    Post subject: Reply with quote

Jayagee,

I don't see the X-wing, either. My column 8 has a third 1 in r7c8. How did you get rid of that?

Have made halting progress. Once the (1,6) Type 1 UR exclusions are made from r6c6, there is a multi-colouring chain on 6's that excludes 6 from r5c6. That gets me 2/3's of the way to that elusive (possibly) phantom XY-wing.

Code:

 *-----------------------------------------------------------*
 | 5     89    48    | 16    49    16    | 3     7     2     |
 | 16    2     7     | 8     3     5     | 9     4     16    |
 | 39    36    14    | 2     49    7     | 8     16    5     |
 |-------------------+-------------------+-------------------|
 | 4     36    9     | 7     2     136   | 16    5     8     |
 | 16    5     2     | 4     8     19    | 167   3     79    |
 | 38    7     18    | 16    5     39    | 2     169   4     |
 |-------------------+-------------------+-------------------|
 | 2     89    5     | 3     16    4     | 167   1689  79    |
 | 7     4     3     | 9     16    8     | 5     2     16    |
 | 89    1     6     | 5     7     2     | 4     89    3     |
 *-----------------------------------------------------------*


Just saw Marty's new post while I was writing this one. Most of the people that I know that do Sudoku are geezers. I'm glad to be included amongst them.
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Thu Aug 24, 2006 3:34 am    Post subject: Reply with quote

One way forward from the position Tracy first posted
Code:

 *-----------------------------------------------------------*
 | 5     89    48    | 16    49    16    | 3     7     2     |
 | 16    2     7     | 8     3     5     | 9     4     16    |
 | 39    36    14    | 2     49    7     | 8     16    5     |
 |-------------------+-------------------+-------------------|
 | 4     36    9     | 7     2     136   | 16    5     8     |
 | 16    5     2     | 4     8     169   | 167   3     79    |
 | 38    7     18    | 16    5     1369  | 2     169   4     |
 |-------------------+-------------------+-------------------|
 | 2     89    5     | 3     16    4     | 167   1689  79    |
 | 7     4     3     | 9     16    8     | 5     2     16    |
 | 89    1     6     | 5     7     2     | 4     89    3     |
 *-----------------------------------------------------------*

is to use the XY-chain r4c2 r6c1 r6c3 r6c4 which eliminates 6 from r4c6.

After that the XY-wing r5c1 r4c2 r4c6 eliminates 1 from r5c6. Also the fork (aka the sashimi variation of a finned X-wing) for 6 based on rows three and four eliminates 6 from r6c8.

The rest is straightforward.

Steve
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Thu Aug 24, 2006 8:00 am    Post subject: Reply with quote

I am not sure if I qualify as an old geezer yet but my wife will not doubt beg to differ.

Anyway, could somebody please look at my previous post concerning the cells at R7C28 and R9C18 on Tracey's posting. At the moment these cells contain the candidates (89), (1689), (89) and (89). If they were all to contain just (89), would this constitute some form of 'deadly pattern' and hence force R7C8 to be (16) ??
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Aug 24, 2006 12:28 pm    Post subject: Reply with quote

David,

Look at this discussion here (specifically the David Bryant post) for a sort-of answer to your question. They can be removed but not necessarily because it's an almost UR. If an almost UR used the same rules as a UR, then look at cells r7c58 and r8c59. That almost UR says we can remove the (1,6) from r7c8, which would reduce the candidates in that cell to an unacceptably low level.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Aug 24, 2006 2:32 pm    Post subject: Reply with quote

After reading Steve R's post (specifically about his XY-chain) and with inspiration born of desperation (and a tip of the hat to David Bryant, Keith and Marty R for the realization that I had to construct some sort of chain) I think I figured out a way to get to the XY-wing I used the first time I solved this puzzle.

I left off here:

Code:

 *-----------------------------------------------------------*
 | 5     89    48    | 16    49    16    | 3     7     2     |
 | 16    2     7     | 8     3     5     | 9     4     16    |
 | 39    36    14    | 2     49    7     | 8     16    5     |
 |-------------------+-------------------+-------------------|
 | 4     36    9     | 7     2     136   | 16    5     8     |
 | 16    5     2     | 4     8     19    | 167   3     79    |
 | 38    7     18    | 16    5     39    | 2    (1)69  4     |
 |-------------------+-------------------+-------------------|
 | 2     89    5     | 3     16    4     | 167   1689  79    |
 | 7     4     3     | 9     16    8     | 5     2     16    |
 | 89    1     6     | 5     7     2     | 4     89    3     |
 *-----------------------------------------------------------*


Using an XY-chain, starting with the (6) in r3c8 => r2c9 => r2c1 => r3c2 => r4c2 => r4c7 ends with the (6) in r4c7, which means that r6c8 can't be 1. (You can tell by my notation that I don't do chains very often). And now we have a (1,6,9) XY-wing with r6c4 as the stem cell that means r5c9 has to be 7, which solves the puzzle.
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jayagee



Joined: 26 Feb 2006
Posts: 7
Location: sunny north dakota

PostPosted: Fri Aug 25, 2006 1:41 am    Post subject: Reply with quote

Tracy: I see what you mean.. I eliminated the 16 from r6,c6 because of the 16 pairs at r1,c4,c6 and r6,c4. Then I decided i had a triple in c6 consisting of 13,19,and 39 in r4,5,&6 respectively. Now I think that may have been false logic even tho it proved out. That yeilds 6 at r6,c4 and clears the 16 pairs in box b. Then my x-wing of 1,s works. I'm pretty sure I've lost my wits the more I stare at this #^*@ thing. Time to use the shredder i,m thinkin.
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Fri Aug 25, 2006 5:13 pm    Post subject: Reply with quote

Tracey

Thanks. That's a good point about the (other) 'almost UR', clearly false assumptions on my behalf. I will now read the piece from David Bryant et al and see if I can follow their logic.

Jayagee

I don't think your triple works unfortunately. I think it's back to school for the both of us.
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Thu Aug 31, 2006 8:35 am    Post subject: Reply with quote

Thanks for that clean, concise explanation, Steve - my 1st encounter with an XY-chain.
Nobody mentioned it, but there is a small technique available here. Once you've used a UR to kill the 16 in R6C6, in rows 3 & 6 there are just two 6s. So there can be no other 6s in column 8 - it kills the 6 in r7c8. (This doesn't otherwise help towards a solution.) I think of this little beast as a partial X-wing. Does it merit its own name?
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