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BUG+2

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Wed Dec 12, 2007 5:54 am    Post subject: BUG+2 Reply with quote
Code:

+---------+---------+------------+
| 8 3  6  | 25 4 15 | 27 1279 19 |
| 4 79 79 | 8  3 12 | 5  12   6  |
| 2 1  5  | 9  6 7  | 3  8    4  |
+---------+---------+------------+
| 5 8  3  | 7  1 9  | 6  4    2  |
| 9 6  4  | 3  2 8  | 1  5    7  |
| 1 27 27 | 6  5 4  | 9  3    8  |
+---------+---------+------------+
| 6 4  8  | 25 9 3  | 27 127  15 |
| 7 5  29 | 1  8 6  | 4  29   3  |
| 3 29 1  | 4  7 25 | 8  6    59 |
+---------+---------+------------+

Play this puzzle online at the Daily Sudoku site

Note that there are only two non-bivalue cells, r1c8 and r7c8. Removing 12 from r1c8 creates a DP, as does removing 2 from r7c8. Using the 2 in either cell results in a contradiction and solving r1c8 =1 solves the puzzle.

I don't recall seeing any BUG discussions when there was a four-candidate cell involved. Was my reasoning valid and can one always try the BUG technique when there are four-candidate cells?

(A brief perusal of the grid will reveal several easy solutions).
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
PostPosted: Wed Dec 12, 2007 2:20 pm    Post subject: Reply with quote
Your reasoning is perfectly sound. Only one point comes to mind. There is no need to check that removing 12 from r1c8 creates a deadly pattern, for example. It is sufficient that eliminating 12 from r1c8 and, at the same time, eliminating 2 from r7c8 does so.

I don’t think there is much mileage in looking for a firm rule limiting the number of non-BUG candidates in a cell although I suspect there is one. I can’t manage five candidates in a BUG but here is an early example involving two cells with four candidates:
Code:

+-----------------+------------------+----------------+
| 69   35   49    | 56+49 1     2    | 34   7    8    |
| 26+9 38   28+49 | 69+4  7     49   | 34   5    1    |
| 7    45   1     | 3     8     45   | 2    9    6    |
+-----------------+------------------+----------------+
| 8    6    59    | 7     23    35   | 1    4    29   |
| 4    2    7     | 8     9     1    | 6    3    5    |
| 59   1    3     | 45+2  24    6    | 7    8    29   |
+-----------------+------------------+----------------+
| 3    9    6     | 1     5     7    | 8    2    4    |
| 25   7    45+2  | 24    6     8    | 9    1    3    |
| 1    48   28+4  | 29+4  34+2  39+4 | 5    6    7    |
+-----------------+------------------+----------------+

Steve
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Wed Dec 12, 2007 5:22 pm    Post subject: Reply with quote
Thank you Steve.
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