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Humbled Again!

 
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dejsmith



Joined: 23 Oct 2005
Posts: 40

PostPosted: Mon Dec 12, 2005 7:11 pm    Post subject: Humbled Again! Reply with quote

Every time I start feeling confident I can handle the "very hards", I am brought back to reality. I certainly hope this one requires some higher level of coloring or something because I'll beat myself up if it turns out I overlooked an obvious! This came from my Saturday, 12/10 paper.

000 602 080
000 000 015
403 010 000

800 007 004
001 020 600
700 900 002

000 030 807
160 000 000
070 408 000

I got to this point:

010 602 080
600 003 015
403 010 006

800 007 004
001 324 678
700 980 002

200 030 807
168 270 040
370 408 001

By the way I want to thank Someone, David, & Alan for all their help & suggestions & comments on this site. I was getting kind of snooty about doing easy & medium ones until you guys got me to attempt them without marking up my grids. I keep all of the ones I screw up on & review your comments to try to get better. Thanks also to Samgj for maintaining this site!

Dave Smith
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Mon Dec 12, 2005 7:55 pm    Post subject: This one needs coloring. Reply with quote

Hi, Dave! Thanks for the kind words.

This puzzle also appeared in the Denver paper on Saturday, so I've worked through it a couple of times already. You do need coloring to complete it -- or at least, that's the only technique that worked for me.

First for the easy moves -- I'm going through this because you haven't indicated which possibilities you've managed to eliminate. Anyway, at this point you should have managed to identify several pairs and a triplet:

-- there's a pair {7, 8} in r2c4 & r3c4, and another pair {1, 5} in r4c4 & r8c4.
-- there's a pair {5, 9} in r3c6 & r8c6, and another pair {1, 6} in r6c6 & r7c6.
-- there's a pair {3, 9} in r1c9 & r8c9.
-- the triplet {4, 5, 9} occupies r1c5, r2c5, & r3c6.
-- the only possibilities in r3c7 & r3c8 are {2, 7, 9} and {2, 9}, respectively.

OK, now for the tricky part. The key is the {3, 9} pair in column 9, which is coupled with the {5, 9} pair in column 6. Looking at these you can see two implication chains:

r1c9 <> 9 ==> r8c9 = 9 ==> r8c6 <> 9 ==> r3c6 = 9
r3c6 <> 9 ==> r8c6 = 9 ==> r8c9 <> 9 ==> r1c9 = 9

So either there's a "9" in r3c6, or else there's a "9" in r1c9. Either way there cannot be a "9" in r3c7 or r3c8. So you can conclude that r3c8 = 2, and r3c7 = 7 -- from there you can place a couple of numbers in the top center 3x3 box, and you can complete the top left 3x3 box, and it should be pretty much ho-hum from there. dcb

PS This was definitely the tough spot in this puzzle for me. The two pairs involving "9" in columns 6 and 9 form a sort of lop-sided X-Wing, which is the way I was finally able to visualize it.

PPS Oh -- I should explain why I think of this as a "coloring" solution. I'm taking the terminology, "multi-coloring," from Angus Johnson. Let's put colors on the four cells -- r1c9 is blue, r8c9 is green, r8c6 is pink, and r3c6 is orange. Then we can visualize the implication chains above as "if blue is false, then orange is true" and "if orange is false, then blue is true."


Last edited by David Bryant on Tue Dec 13, 2005 1:35 pm; edited 1 time in total
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Mon Dec 12, 2005 8:24 pm    Post subject: Reply with quote

Hi Dave,

Starting from:
Code:
  . 1 . 6 . 2 . 8 .
  6 . . . . 3 . 1 5
  4 . 3 . 1 . . . 6
  8 . . . . 7 . . 4
  . . 1 3 2 4 6 7 8
  7 . . 9 8 . . . 2
  2 . . . 3 . 8 . 7
  1 6 8 2 7 . . 4 .
  3 7 . 4 . 8 . . 1

5 not in r4c2, not in r4c3, not in r6c2, not in r6c3,
because it is in r5c1 or r5c2 (Row on 3x3 Block interaction)

9 not in r4c2, not in r4c3,
because it is in r5c1 or r5c2 (Row on 3x3 Block interaction)

3 not in r4c7, not in r6c7,
because it is in r4c8 or r6c8 (Column on 3x3 Block interaction)

5 not in r3c4, Hidden Pair 7 8 in r2c4 and r3c4 (in Column)

5 not in r6c6, not in r7c6,
becasue of Hidden Pair 7 8 in r2c4 and r3c4 (in Column)

9 not in r7c6, Hidden Pair 1 6 in r6c6 and r7c6 (in Column)

5 not in r4c7, not in r4c8,
because it is in r6c7 or r6c8 (Row on 3x3 Block interaction)

2 not in r3c2, XY-Wing X=3 Y=9 in r4c8 X=3 Z=2 in r4c2 Y=9 Z=2 in r3c8

2 not in r2c7, it is in r3c7 or r3c8 (Row on 3x3 Block interaction)

And from here we apply the technique: "Double implication Chain for Pairs"

digit 9 from r3c7 and r3c8 can be excluded
because they force r1c9 = 3, r8c9 = 9 in one chain
and r3c6 = 5, r8c6 = 9 in the second chain
and of course r8c9 and r8c6 can not have both digit 9
(see the following candidate table):
Code:
59  1   579 6  459  2   3479 8    39   
                                  Ba   
6   289 279 78 49   3   479  1    5   
                        ..a           
4   589 3   78 1    59  279  29   6   
                    Ba  ..*  a*       
8   23  26  15 56   7   19   39   4   
   
59  59  1   3  2    4   6    7    8   
 
7   34  46  9  8    16  15   35   2   
   
2   459 459 15 3    16  8    569  7   
 
1   6   8   2  7    59  359  4    39   
                    .B            .B   
3   7   59  4  569   8  259  2569 1   


and the rest is only standard training, up to the solution:
Code:
  5 1 7 6 4 2 3 8 9
  6 8 2 7 9 3 4 1 5
  4 9 3 8 1 5 7 2 6
  8 2 6 1 5 7 9 3 4
  9 5 1 3 2 4 6 7 8
  7 3 4 9 8 6 1 5 2
  2 4 9 5 3 1 8 6 7
  1 6 8 2 7 9 5 4 3
  3 7 5 4 6 8 2 9 1


hope I could help you,

P.S. one more time David was better than me. He posted his solution quicker! Where is Alan? Wink
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Mon Dec 12, 2005 8:40 pm    Post subject: I had an unfair advantage! Reply with quote

Someone_Somewhere wrote:
P.S. one more time David was better than me. He posted his solution quicker!

Well, I had an advantage -- as I mentioned, this puzzle appeared in my local newspaper last Saturday. So I had just recently worked through it, and got stuck at just about the same spot as our friend Dave Smith got to. dcb Smile
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dejsmith



Joined: 23 Oct 2005
Posts: 40

PostPosted: Mon Dec 12, 2005 10:05 pm    Post subject: More Study Required! Reply with quote

Yes, I will do a better job from now on in providing the possibilities I've whittled down with my grid as I did have all the pairs & things. Your solutions seems so easy after the fact. My confidence is high with X Wings & most XY Wings; but this technique goes in my keeper & study harder pile!!! Thanks.

Dave Smith
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dotdot



Joined: 07 Dec 2005
Posts: 29
Location: oberseen

PostPosted: Sun Dec 18, 2005 3:14 pm    Post subject: ramblers and rock climbers Reply with quote

I thought I would try this one out too, to get some experience of these advanced situations.
So I plodded along in my unadventurous manner, all the time expecting defeat just around the next corner. Plodded along, no lookahead, no wings or whatever, and arrived at the top with no special story to tell.

Some sudoku landscapes may have well trodden paths, but this one apparently offers lots of significantly different routes.

And don't ask me what way I went.
My second (plodding) attempt would probably be quite different in sequence and therefore in character.
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