## Question about Forcing Chains

Advanced methods and approaches for solving Sudoku puzzles

### Question about Forcing Chains

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 => 2r4c57r4c2->2r8c2->2r7c6->2r4c57r4c5->7r8c6->2r8c2->2r7c6->2r4c57r4c6->2r4c5Row 4 must contain a 7every possibility results in 2r4c5therefore r4c5 is a 2Is this guessing?How can this be shown in an aic?`
dan

ArkieTech

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Location: NW Arkansas USA

### Re: Question about Forcing Chains

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?

Luke
2015 Supporter

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### Re: Question about Forcing Chains

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
dan

ArkieTech

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Joined: 29 May 2006
Location: NW Arkansas USA

### Re: Question about Forcing Chains

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

Luke
2015 Supporter

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Location: Southern Northern California

### Re: Question about Forcing Chains

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

OOPs back to the drawing board....

thanks.
dan

ArkieTech

Posts: 3240
Joined: 29 May 2006
Location: NW Arkansas USA

### Re: Question about Forcing Chains

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 !
JC Van Hay

Posts: 719
Joined: 22 May 2010

### Re: Question about Forcing Chains

Wow, JC, excellent post. I particularly like the use of *memory in the kraken row.

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

### Re: Question about Forcing Chains

[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.
daj95376
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### Re: Question about Forcing Chains

[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`
daj95376
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