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Rambling: Trivial BUG+2 Scenario

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Oct 24, 2010 4:38 pm    Post subject: Rambling: Trivial BUG+2 Scenario Reply with quote
From time-to-time, I run across something that I'd never given any previous thought. So, I'm going to start a Rambling thread when I see something interesting but not significant.

While reading a thread in another forum about BUG+n eliminations, I ran across two scenarios where a BUG+2 existed in two peer cells. In both cases, there was a trivial elimination present that was not part of the solution in the other forum. Consider the following two grids and the inherent strong link.

Code:
 (2)r6c1 = (8)r6c9  =>  r6c1<>8 and r6c9<>2 (if it existed)
 +-----------------------------------------------------+
 |  3    7    1    |  4    6    5    |  9    8    2    |
 |  24   9    45   |  27   1    8    |  57   3    6    |
 |  6    25   8    |  27   9    3    |  1    4    57   |
 |-----------------+-----------------+-----------------|
 |  1    56   59   |  3    78   2    |  4    67   89   |
 |  28   3    7    |  9    4    6    |  25   1    58   |
 |  48+2 26   49   |  5    78   1    |  23   67   39+8 |
 |-----------------+-----------------+-----------------|
 |  9    1    2    |  6    3    7    |  8    5    4    |
 |  5    8    6    |  1    2    4    |  37   9    37   |
 |  7    4    3    |  8    5    9    |  6    2    1    |
 +-----------------------------------------------------+
 # 26 eliminations remain

Code:
 (2)r9c1 = (9)r9c2  =>  r9c1<>9 (if it existed) and r9c2<>2
 +-----------------------------------------------------+
 |  6    1    8    |  9    7    2    |  5    3    4    |
 |  3    4    79   |  5    1    8    |  26   29   67   |
 |  27   29   5    |  4    3    6    |  1    89   78   |
 |-----------------+-----------------+-----------------|
 |  45   35   34   |  7    2    1    |  8    6    9    |
 |  1    8    2    |  6    4    9    |  3    7    5    |
 |  9    7    6    |  3    8    5    |  4    1    2    |
 |-----------------+-----------------+-----------------|
 |  25   56   34   |  1    9    34   |  7    28   68   |
 |  8    69   1    |  2    5    7    |  69   4    3    |
 |  47+2 23+9 79   |  8    6    34   |  29   5    1    |
 +-----------------------------------------------------+
 # 26 eliminations remain

[Edit: changed the title slightly.]

Last edited by daj95376 on Mon Oct 25, 2010 12:21 am; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Oct 24, 2010 5:24 pm    Post subject: Reply with quote
I don't follow because of my usual difficulties with notation, as opposed to words, but all BUG+2 conditions that I've seen can be easily solved by creating a pincer situation and the two grids above are no exception. Plus the second grid has the 29 pseudo cell to knock out the 9 from r9c3.

I'm not sure if this has any relevance to what you intended with this thread.
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK
PostPosted: Sun Oct 24, 2010 7:51 pm    Post subject: Reply with quote
Danny, interesting - do you think these eliminations might ever be possible only from that strong link logic - or will, as in this case, there always be external simple deductions that make the same eliminations?

So in #1
Code:
(2)r6c1 - (2=8)r5c1 ; r6c1<>8
(8)r6c9 - (8=5)r5c9 - (5=2)r5c7 ; r6c9<>2 (if existed)
and #2
As marty pointed out, the (29)r9c7 makes the eliminations externally (so to speak)
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Mon Oct 25, 2010 12:29 am    Post subject: Reply with quote
Thses BUG+2 examples are not limited to one way of advancing the puzzle. I doubt if any BUG+2 is limited to just one approach.

In the first example, the <2> and <8> can be combined with <6> and <7> in [r6] to form a pseudo- Naked Quad, which was in the solution I saw for the puzzle. Peter demonstrated a third approach.

My objective was to demonstrate BUG+2 logic that I don't recall having seem previously.
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ronk



Joined: 07 May 2006
Posts: 398
PostPosted: Mon Oct 25, 2010 5:49 pm    Post subject: Re: Rambling: Trivial BUG+2 Scenario Reply with quote
daj95376 wrote:
While reading a thread in another forum about BUG+n eliminations, I ran across two scenarios where a BUG+2 existed in two peer cells. In both cases, there was a trivial elimination present that was not part of the solution in the other forum.

Code:
 (2)r6c1 = (8)r6c9  =>  r6c1<>8 and r6c9<>2 (if it existed)
 +-----------------------------------------------------+
 |  3    7    1    |  4    6    5    |  9    8    2    |
 |  24   9    45   |  27   1    8    |  57   3    6    |
 |  6    25   8    |  27   9    3    |  1    4    57   |
 |-----------------+-----------------+-----------------|
 |  1    56   59   |  3    78   2    |  4    67   89   |
 |  28   3    7    |  9    4    6    |  25   1    58   |
 |  48+2 26   49   |  5    78   1    |  23   67   39+8 |
 |-----------------+-----------------+-----------------|
 |  9    1    2    |  6    3    7    |  8    5    4    |
 |  5    8    6    |  1    2    4    |  37   9    37   |
 |  7    4    3    |  8    5    9    |  6    2    1    |
 +-----------------------------------------------------+
 # 26 eliminations remain

Using the quantum naked quad of that forum (<2678> in r6c13589), the valid exclusions are r6c1<>8 and r6c7<>2.

The untouchables are the candidates that comprise the set, not all the candidates of the involved cells. Using the above naked quad, therefore, <48> of r6c1 and <39> of r6c9 are "free game."
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