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A real stumper from local newspaper

 
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jayagee



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

PostPosted: Wed Aug 02, 2006 2:10 am    Post subject: A real stumper from local newspaper Reply with quote

Puzzle as published

XX9 53X 4X8
XXX XXX X91
XX5 XX6 XX3
XXX 9XX X17
XXX XXX XXX
61X XX8 XXX
5XX 7XX 9XX
38X XXX XXX
9X1 X23 X8X

I got this far and can't find any logical way to solve. I did solve by using trial and error or colors but that seemed like cheating. What am I missing?

1X9 53X 468
XXX 8XX 591
845 196 XX3
XXX 96X X17
XXX XXX XXX
61X XX8 X5X
5XX 781 93X
38X 659 1XX
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Aug 02, 2006 8:36 am    Post subject: Reply with quote

The puzzle as you posted it, has no solution - though this is not obvious (at the end you get cells without possible candidates).
In the second grid you posted (last row missing) there are a lot of singles, e.g. r5c5=1, r5c2=9 , r6c9=9....
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David Bryant



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

PostPosted: Wed Aug 02, 2006 12:19 pm    Post subject: I think there's a typo Reply with quote

Hi, jayagee! Welcome to the forum.

I think there's a typo in your original grid -- it's asymmetrical. I think it ought to look like this.

X9X 53X 4X8
XXX XXX X91
XX5 XX6 XX3
XXX 9XX X17
XXX XXX XXX
61X XX8 XXX
5XX 7XX 9XX
38X XXX XXX
9X1 X23 X8X

With this correction the puzzle has a unique solution, and all the numbers you showed in your second grid appear to be correct. So I think this is where you're stuck.

19X 53X 468
XXX 8XX 591
845 196 XX3
XXX 96X X17
XXX XXX XXX
61X XX8 X5X
5XX 781 93X
38X 659 1XX
9X1 423 X85

Here there's one obvious move -- r5c5 = 1 (there's a naked pair {4, 7} in column 5, at r2c5 & r6c5).

The next thing I noticed is a "fork" on the digit 7 ... you can only enter a "7" in two places in row 1 (r1c3 or r1c6) and "7" will only fit in two spots in column 1 (r2c1 & r5c1). So either r1c6 = 7, or else r5c1 = 7. Either way there cannot possibly be a "7" at r5c6. So the "7" in the middle center 3x3 box has to be at r6c5, and the rest of the puzzle is straightforward. dcb
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jayagee



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

PostPosted: Wed Aug 02, 2006 12:27 pm    Post subject: Reply with quote

You are right on about the typo...and I did have the 1 at r5,c5 but somehow left it out when I posted. Totally missed the "fork" you pointed out. Hadn't seen this type of thing before. Thanks a bunch. You made it look easy.
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David Bryant



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

PostPosted: Wed Aug 02, 2006 1:17 pm    Post subject: Practice, practice, practice ... Reply with quote

jayagee wrote:
Thanks a bunch. You made it look easy.

You're welcome. It's not exactly easy, though. I've had a lot of practice. Smile

The "fork" is an advanced technique. It's also called "multi-coloring", and "fishy cycle". You can read more about that technique on Ruud's excellent website. dcb
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Aug 02, 2006 2:17 pm    Post subject: Reply with quote

(Hurry, before Keith comes Smile )
Code:
 1    9     27  |  5    3    27  |  4     6    8         
 27   36    36  |  8    47   247 |  5     9    1         
 8    4     5   |  1    9    6   |  27    27   3 
--------------------------------------------------
 24   235   238 |  9    6    45  |  238   1    7         
 247  2357  89  |  23   1    457 |  68    24   69         
 6    1     79  |  23   47   8   |  23    5    49   
--------------------------------------------------   
 5    26   #246 |  7    8    1   |  9     3   #246       
 3    8    #247 |  6    5    9   |  1     47  #24         
 9    67    1   |  4    2    3   |  67    8    5       

There is an alternative for the fork (there are at least 5 forks for 7):
Look at the UR 24 in r78c39. There are strong links for 4 in row 7 and column 3 and for 2 in row 8. Therefore the 2's in r7c39 can be eliminated:

r7c3=2 => r7c9=4 and r8c3=4 => r8c9=2
r7c9=2 => r7c3=4 and r8c9=4 => r8c3=2

With the strong link for 2 in column 9 you can also eliminate 4 from r8c9 and 2 from r8c3:
r8c9=4 => r7c9=2 and r8c3=2 => r7c3=4
r8c3=2 => r7c3=4 and r8c9=4 => r7c9=2

In all cases you get a deadly pattern.

Or an AUR:
r7c2=6 => r9c2=7 => deadly pattern.

PS: But i saw now that (as often) it does not solve it Sad
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