SudoCue Users

Posted: **Sat Jul 08, 2006 7:18 pm**

Today's Nightmare is kind of special!

000001607908070010020000000036005000004060900000200460000000050090030108802700000

Applying the usual, plus an XY-wing and a Type 2 UR, you get here:

Code: Select all

+----------------------+----------------------+----------------------+
| 34     45     35     | 89     289    1      | 6      289    7      | 
| 9      6      8      | 345    7      24     | 25     1      234    | 
| 7      2      1      | 345689 4589   4689   | 58     3489   349    | 
+----------------------+----------------------+----------------------+
| 12     3      6      | 49     49     5      | 78     78     12     | 
| 125    78     4      | 18     6      37     | 9      23     1235   | 
| 15     78     9      | 2      18     37     | 4      6      135    | 
+----------------------+----------------------+----------------------+
| 346    14     37     | 14689  12489  24689  | 27     5      2469   | 
| 46     9      57     | 456    3      246    | 1      247    8      | 
| 8      15     2      | 7      15     469    | 3      49     469    | 
+----------------------+----------------------+----------------------+

Take a look at R456C19, and consider the following:

The pattern

Code: Select all

12  | 12
125 | 125
15  | 15

Has two solutions:

Code: Select all

1 | 2
2 | 5
5 | 1

and

2 | 1
5 | 2
1 | 5

Note how three values in the columns may be interchanged to get the two solutions.

So, in the position posted above, one of R56C9 must be <3>; R5C8 and R23C9 cannot be <3>.

These eliminations solve the puzzle. (Actually, eliminating <3> from only one of R5C8 or R2C9 solves the puzzle!)

Otherwise, it seems, the path to the solution is still quite difficult. Sudoku Susser needs four chains (with 6, 11, 4, and 5 links) and an XY-wing.

Keith

Posted: **Sat Jul 08, 2006 9:34 pm**

Good catch, Keith!

There is the BUG-Lite to get you in the mood for BUG-week!

Ruud

Posted: **Sun Jul 09, 2006 12:13 am**

Ruud,

This is a BUG-Lite

Clearly, I am about to learn something

Keith

Posted: **Sun Jul 09, 2006 6:56 am**

You can probably put this in the picking nits department

Actually, since you are avoiding more than two base digits per cell, it qualifies as a MUG rather than a BUG-Lite

Code: Select all

abc | abc
abc | abc
abc | abc

...This is the underlying deadly MUG pattern in this case. Note that not every candidate has to be in every cell--such is the case in your example.

Here is a very similar BUG-Lite, but it is not quite the same...

Code: Select all

ab | ab
bc | bc
ac | ac

Here is a post where I made a lot of mistakes trying to compose MUGs from multiple UR's/BUG-Lites.

http://www.sudoku.com/forums/viewtopic. ... ght=#21050

...and here is another mistake riddled post on BUG-Lites

.
http://www.sudoku.com/forums/viewtopic. ... ght=#19843

Posted: **Sun Jul 09, 2006 11:41 pm**

An alternative solution appears when you notice that block 7 is a crossroads for several implication chains, for which R8C3 can be taken as a root. Setting R8C3 to 7 forces a contradiction in '5' at R3C57 so R8C3=5, leading directly to the solution.

SudoCue Users

July 8 Nightmare

July 8 Nightmare

This is a BUG-Lite?