Question about Forcing Chains

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Question about Forcing Chains

Postby ArkieTech » Sat Jan 26, 2013 4:59 pm

Code: Select all
 *-----------------------------------------------------------------------------*
 | 3789    34789   79      | 1       34579   34579   | 6       2       348     |
 | 6       2347    1       | 247     2347    8       | 9       34      5       |
 | 2389    23489   5       | 24      6       2349    | 1       348     7       |
 |-------------------------+-------------------------+-------------------------|
 | 4       578     6       | 3       1257    257     | 58      9       18      |
 | 3789    35789   2       | 4578    14579   4579    | 358     135678  1368    |
 | 3789    1       79      | 578     579     6       | 4       3578    2       |
 |-------------------------+-------------------------+-------------------------|
 | 5       29      3       | 6       8       24      | 7       14      149     |
 | 1       27      4       | 9       2357    2357    | 2358    3568    368     |
 | 279     6       8       | 2457    23457   1       | 235     345     349     |
 *-----------------------------------------------------------------------------*

FC:7r4 => 2r4c5
7r4c2->2r8c2->2r7c6->2r4c5
7r4c5->7r8c6->2r8c2->2r7c6->2r4c5
7r4c6->2r4c5

Row 4 must contain a 7
every possibility results in 2r4c5
therefore r4c5 is a 2

Is this guessing?

How can this be shown in an aic?
dan
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Re: Question about Forcing Chains

Postby Luke » Sat Jan 26, 2013 5:35 pm

This looks like kraken row to me.

Also, the middle figure is lost on me....if r4c5 is 7, then r4c5 is 2? How does that work?
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Re: Question about Forcing Chains

Postby ArkieTech » Sat Jan 26, 2013 5:50 pm

Luke451 wrote:This looks like kraken row to me.

Also, the middle figure is lost on me....if r4c5 is 7, then r4c5 is 2? How does that work?


if r4c5 is 7 then -7r45c6->7r8c6->2r8c2->-2r7c2->2r7c6->-2r4c6->2r4c5

I'll study up on kraken row :D
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Re: Question about Forcing Chains

Postby Luke » Sat Jan 26, 2013 5:55 pm

Thanks, Dan. But, are you sure you're not overlooking (7)r1c6?
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Re: Question about Forcing Chains

Postby ArkieTech » Sat Jan 26, 2013 6:51 pm

Luke451 wrote:Thanks, Dan. But, are you sure you're not overlooking (7)r1c6?



OOPs back to the drawing board.... :oops:

thanks.
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Re: Question about Forcing Chains

Postby JC Van Hay » Sat Jan 26, 2013 7:17 pm

There are several equivalent ways to prove an elimination or a placement !

Here : -2r4c6 (or +2r4c5) can be proved by using 5 SIS : 7R248 R8C2 2R7.
Code: Select all
+------------------+-------------------------+--------------------+
| 3789  34789   79 | 1       34579    34579  | 6     2       348  |
| 6     234(7)  1  | 24(7)   234(7)   8      | 9     34      5    |
| 2389  23489   5  | 24      6        2349   | 1     348     7    |
+------------------+-------------------------+--------------------+
| 4     58(7)   6  | 3       125(7)   5-2(7) | 58    9       18   |
| 3789  35789   2  | 4578    14579    4579   | 358   135678  1368 |
| 3789  1       79 | 578     579      6      | 4     3578    2    |
+------------------+-------------------------+--------------------+
| 5     9(2)    3  | 6       8        4(2)   | 7     14      149  |
| 1     (27)    4  | 9       235(7)   235(7) | 2358  3568    368  |
| 279   6       8  | 245(7)  2345(7)  1      | 235   345     349  |
+------------------+-------------------------+--------------------+

1. As a "Transfer Matrix" (the most general way-vertically written "chain" to show explicitly all the relations between candidates) :

Code: Select all
2r7c6=2r7c2
      2r8c2=7r8c2
            7r8c56=7r9c45
            7r2c2==7r2c45
            7r4c2==7r4c5==7r4c6

-> 2r7c6=7r4c6 :=> -2r4c6

2. As a Kraken Row 7R4 -> 2r7c6=7r4c6 :=> -2r4c6

7r4c2-(7=2)r8c2-2r7c2=2r7c6
||
7r4c5-7r289c5=*[7r8c6=*7r9c4-7r2c4=*7r2c3]-(7=2)r8c2-2r7c2=2r7c6
||
7r4c6

3. As an AIC : As 7R24B8 is an almost finned swordfish (the fin is 7r8c6) ... =>
Chain[5] : 7r4c6=FinnedSwordfish(7R24B8)-(7=2)r8c2-2r7c2=2r7c6 :=> -2r4c6

Is this guessing?

No comment :D!
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Re: Question about Forcing Chains

Postby Luke » Sat Jan 26, 2013 9:17 pm

Wow, JC, excellent post. I particularly like the use of *memory in the kraken row.
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Re: Question about Forcing Chains

Postby daj95376 » Sat Jan 26, 2013 10:11 pm

[Edit: given recent discussions, I'm specifically using Forcing Chains ala Jeff.]

A Kraken Row/Column/Box translates into a forcing chain in my book. (four inference streams)

Code: Select all
 +--------------------------------------------------------------------------------+
 |  3789    34789   79      |  1       34579  *34579   |  6       2       348     |
 |  6       2347    1       |  247     2347    8       |  9       34      5       |
 |  2389    23489   5       |  24      6       2349    |  1       348     7       |
 |--------------------------+--------------------------+--------------------------|
 |  4       578     6       |  3       1257   *257     |  58      9       18      |
 |  3789    35789   2       |  4578    14579  *4579    |  358     135678  1368    |
 |  3789    1       79      |  578     579     6       |  4       3578    2       |
 |--------------------------+--------------------------+--------------------------|
 |  5       29      3       |  6       8       24      |  7       14      149     |
 |  1       27      4       |  9       2357   *2357    |  2358    3568    368     |
 |  279     6       8       |  2457    23457   1       |  235     345     349     |
 +--------------------------------------------------------------------------------+
 # 122 eliminations remain

 Kraken Column [c6] on <7>:  r1458c6=7

 (7)r4c6                                               =>  r4c6<>2
 (7)r1c6 - r1c123 = r2c2 - (7=2)r8c2 - r7c2 = (2)r7c6  =>  r4c6<>2
 (7)r5c6 - r4c56  = r4c2 - (7=2)r8c2 - r7c2 = (2)r7c6  =>  r4c6<>2
 (7)r8c6                 - (7=2)r8c2 - r7c2 = (2)r7c6  =>  r4c6<>2
Last edited by daj95376 on Sun Jan 27, 2013 6:18 pm, edited 1 time in total.
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Re: Question about Forcing Chains

Postby daj95376 » Sun Jan 27, 2013 1:08 am

[Edit: given recent discussions, I'm specifically using Forcing Chains ala Jeff.]

Alternate, and more interesting forcing chain perspective. Three of the implication streams merge into a common outcome.

Code: Select all
 +--------------------------------------------------------------------------------+
 |  3789    34789   79      |  1       34579   34579   |  6       2       348     |
 |  6       2347    1       |  247     2347    8       |  9       34      5       |
 |  2389    23489   5       |  24      6       2349    |  1       348     7       |
 |--------------------------+--------------------------+--------------------------|
 |  4       578     6       |  3       1257    257     |  58      9       18      |
 |  3789    35789   2       |  4578    14579   4579    |  358     135678  1368    |
 |  3789    1       79      |  578     579     6       |  4       3578    2       |
 |--------------------------+--------------------------+--------------------------|
 |  5       29      3       |  6       8       24      |  7       14      149     |
 |  1      [27]     4       |  9       2357    2357    |  2358    3568    368     |
 |  279     6       8       |  2457    23457   1       |  235     345     349     |
 +--------------------------------------------------------------------------------+
 # 122 eliminations remain

 (2)r8c2 - r7c2 = r7c6 -                 (2)r4c6

 (7)r8c2 - r12c2 = r1c13 - (7)r1c6 \
         - r4 c2 = r4c56 - (7)r5c6  \
         -                 (7)r8c6   = (7-2)r4c6


AIC w/o details on forcing chain:

Code: Select all
 (2)r7c6 = (2)r7c2 - (2=7)r8c2 -FC- (7)r158c6 = (7)r4c6  =>  r4c6<>2
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