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Help with a BUG-like puzzle

 
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Sun Aug 17, 2008 4:03 am    Post subject: Help with a BUG-like puzzle Reply with quote
This is todays fiendish puzzle from Vanhegan.:

Code:
 *-----------*
 |...|6.9|8.2|
 |.9.|..5|...|
 |..5|..3|...|
 |---+---+---|
 |1..|...|6.8|
 |..6|...|7..|
 |2.4|...|..9|
 |---+---+---|
 |...|2..|1..|
 |...|8..|.7.|
 |3.7|1.6|...|
 *-----------*

Basics get me to this point where I get confused (which is not unusual).

Code:

 
 *-----------------------------------------------------------*
 | 7     4     3     | 6     1     9     | 8     5     2     |
 | 68    9     12    | 47    28    5     | 34    36    17    |
 | 68    12    5     | 47    28    3     | 49    69    17    |
 |-------------------+-------------------+-------------------|
 | 1     3     9     | 5     7     2     | 6     4     8     |
 | 5     8     6     | 9     4     1     | 7     2     3     |
 | 2     7     4     | 3     6     8     | 5     1     9     |
 |-------------------+-------------------+-------------------|
 | 4     56    8     | 2     39    7     | 1     39    56    |
 | 9     1256  12    | 8     35    4     | 23    7     56    |
 | 3     25    7     | 1     59    6     | 29    8     4     |
 *-----------------------------------------------------------*


All cells are bivalue except for r8c2 which has four candidates, not the normal three we (I) associate with a normal BUG situation. In fact, we have three <5>s in box 7, row 8 and column 2 but all in column 2 are restricted to box 7. On the other hand, the <2>s candidate meets all the normal criteria for a BUG. I tried both the <2> and the <5> and thereby know the correct answer, but I don't have a valid explanation.

Would someone please turn on the light! Idea

Ted
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Sun Aug 17, 2008 4:19 am    Post subject: Reply with quote
That is very interesting. I've never seen a BUG+2 with both extra digits in the same cell.

If you remove <2> and <5> from r8c2 a BUG results. So, we know that cell must be <2> or <5>.

However, also look at r78c29: this is a Type 1 UR and r8c2 cannot be <5> or <6>.

Between these two constraints, r8c2 must be 2.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Aug 17, 2008 5:18 am    Post subject: Reply with quote
Just looking at it in a slightly different way, after the UR, the 12 pair in c2 should finish it off.

From a terminology standpoint, isn't that a BUG+1 with the +1 having four rather than the usual three candidates? I've seen BUG+2 (BUG+3) used when there are two (three) non-bivalue cells.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Sun Aug 17, 2008 3:34 pm    Post subject: Reply with quote
Asellus wrote:


However, also look at r78c29: this is a Type 1 UR and r8c2 cannot be <5> or <6>.


Asellus, I was so focused on the BUG that I failed to notice the UR.

In this case the UR deleted one of the extra candidates, but what if that was not possible. As I previously noted, I tried setting r8c2 to both <2> and <5> and found that only the <2> provided a valid solution. Is this T & E the only option if another deletion is not available?

Ted
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ravel



Joined: 21 Apr 2006
Posts: 536
PostPosted: Sun Aug 17, 2008 6:49 pm    Post subject: Reply with quote
Marty R. wrote:
From a terminology standpoint, isn't that a BUG+1 with the +1 having four rather than the usual three candidates? I've seen BUG+2 (BUG+3) used when there are two (three) non-bivalue cells.
I have seen both interpretations of the n in BUG+n, number of extra candidates beyond bivalue cells and number of cells with more than 2 candidates. Not the first terminology problem ...
tlanglet wrote:
As I previously noted, I tried setting r8c2 to both <2> and <5> and found that only the <2> provided a valid solution. Is this T & E the only option if another deletion is not available?
I dont talk again about T&E Smile Its a contradiction chain, but with the UR available, a less elegant way to solve it.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Sun Aug 17, 2008 11:20 pm    Post subject: Reply with quote
tanglet wrote:
Is this T & E the only option if another deletion is not available?

Not at all. Remember: In a Deadly Pattern where the extra digit(s) is(are) confined to a single cell, you are not so much placing the extra digit as removing the potential DP digits. So here, you remove the <1> and <6> from r8c2 and are left with a 25 naked pair that solves the puzzle. No T&E involved.
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