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16 December 2006 Nightmare
Posted: Tue Jan 16, 2007 9:36 pm
by Sudtyro
Don’t have a solver, but got this far manually before stalling out. Can anyone offer a kick-start?
Code: Select all
1 2 567 | 49 3 49 | 56 67 8
8 69 356 | 2 1 7 | 45 36 469
379 79 4 | 6 5 8 | 1 237 29
-------------+---------------+--------------
5 14 9 | 3 7 26 | 8 246 126
26 3 68 | 5 48 1 | 9 246 7
267 14 678 | 48 9 26 | 3 5 126
-------------+---------------+--------------
69 5 1 | 7 2 49 | 46 8 3
367 678 367 | 1 48 5 | 2 9 46
4 89 2 | 89 6 3 | 7 1 5
Posted: Wed Jan 17, 2007 10:22 pm
by Ruud
Hi Sudtyro, welcome to the forum.
This Nightmare can be advanced from this point by 3D coloring. However, there is also an [[ALS-XZ]] move that breaks the puzzle.
Consider r3468c9 with candidates for digits 12469.
Consider r7c17 with candidates for digits 469.
Both sets have one one surplus digit, which makes them Almost Locked Sets.
Both sets have a single candidate for digit 4 in box 9, so one of the sets will NOT contain digit 4 and must contain all remaining digits.
Both sets have a single candidate for digit 9, since one of them must be true (previous rule), r3c1 cannot contain digit 9.
This leads to several singles and your next advanced move.
Ruud
Posted: Thu Jan 18, 2007 12:43 am
by Sudtyro
Thanks for the quick response! I had tried the 3D coloring, but didn't see an immediate way forward. Let me look at the ALS approach...that's a new study area for me. Still much to learn...
Posted: Thu Jan 18, 2007 7:55 pm
by unkx80
Ruud's ALS-XZ is so big.
There is a smaller ALS-XZ, actually a Type 2
WXYZ-Wing. The cells involved are r2c8, r2c2, r3c1, r3c2, leading to r2c3<>3.
Posted: Fri Jan 19, 2007 10:01 pm
by Sudtyro
unkx80 wrote:
There is a smaller ALS-XZ, actually a Type 2
WXYZ-Wing. The cells involved are r2c8, r2c2, r3c1, r3c2, leading to r2c3<>3.
Thanks for the tip...learning fast!