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April 18th: Finding the 56 Pairing in Column 7 ?

 
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jabejochke



Joined: 16 Mar 2006
Posts: 21
Location: Reading

PostPosted: Wed Apr 19, 2006 12:43 pm    Post subject: April 18th: Finding the 56 Pairing in Column 7 ? Reply with quote

For me the breakthru for April 18th's puzzle was finding the 56 pairing at r2c7 and r3c7.

Finding this pair (or 'working it into existence') was both difficult and enlightening while trying to avoid candidate profiling.

To those who found it without profiling, how did it emerge? To those who profiled, how did it show itself? And to those for which this pairing was not the breakthru for this puzzle, what was?

Any comments and insights would be most appreciated. Thanks,

Jack
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Wed Apr 19, 2006 1:13 pm    Post subject: Spotting "hidden pairs" Reply with quote

Hi, Jack!

I have to agree that finding the pair {5, 6} was a crucial step. After entering just a few values I arrived at this position.
Code:
 *-----------*
 |532|68.|..9|
 |1.4|...|...|
 |..7|2..|...|
 |---+---+---|
 |7..|.1.|8..|
 |.91|.6.|.5.|
 |..6|.2.|..1|
 |---+---+---|
 |...|..8|9..|
 |...|..2|3.8|
 |4..|.96|17.|
 *-----------*

One can "see" the {5, 6} pair at this point, but it takes a couple of steps.

-- Clearly the "5" in column 7 lies in the top right 3x3 box, because of the "5" at r5c8.

-- Similarly, the "6" in column 7 lies in the top right 3x3 box, because of "6"s at r5c5 & r6c3.

-- But neither "5" nor "6" can fit at r7c1, leaving the pair in c7r2&3, as you said.

This hidden pair is hard to spot because most of the information about it is embedded in the interactions among rows, columns, and blocks. dcb
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PostPosted: Thu Apr 20, 2006 12:51 pm    Post subject: Reply with quote

David,

Thanks again!

I think the logic you described was the way I got there - though I wasn't able to put it into words.

In thinking about your words, it also dawned on me the implications of the 'blocking' effect of the 9,3,1 in column 7 at rows 7,8 & 9 respectively. It would seem that a configuration showing all completed row or column cells within a block is a situation to be checked out prior to committing to profiling.

Right now, my focus (after doing line_block interactions and mandatory pairs on 5+ rcb's) is to work on the already identified pairs on the board prior to committing to profiling. As you and others have documented there are configurations that can be recognized for breakthru's at this point (example possibly being the 6,8 in row 1 at columns 4 & 5 and its impact on block 1). I think I just learned that checking out these 'blocking 3's' may also be a configuration to be worked before profiling.

Again, thank you again

Jack
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dotdot



Joined: 07 Dec 2005
Posts: 29
Location: oberseen

PostPosted: Thu Apr 20, 2006 12:58 pm    Post subject: premature disclosure Reply with quote

jabejochke wrote:
To those who found it without profiling, how did it emerge?

For me, being a few days behind, this topic title was a spoiler.
So it didn't emerge.
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jabejochke



Joined: 16 Mar 2006
Posts: 21
Location: Reading

PostPosted: Thu Apr 20, 2006 1:40 pm    Post subject: Reply with quote

dotdot,


Quote:
For me, being a few days behind, this topic title was a spoiler


My apology, I will make sure it doesn't happen again.

Jack
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jabejochke



Joined: 16 Mar 2006
Posts: 21
Location: Reading

PostPosted: Thu Apr 20, 2006 1:48 pm    Post subject: Reply with quote

Quote:
checking out these 'blocking 3's' may also be a configuration to be worked before profiling


Since adding this earlier note (inadvertently, as guest), another 'light' dawned. Often in the discussions, I have seen references to 'value-based' or 'positional' configurations -- I guess this 'blocking 3's' would be an example of a positional configuration -- the specific values don't matter.

It takes a while for some of us....but it's worth it.

Jack
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