## Help With Grouping Digital Forcing Chains

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### Help With Grouping Digital Forcing Chains

Below is a Digital Forcing Chain and taken from Scanraid. The rating on this puzzle was 1227. And there were several other Digital Forcing Chains of equal complexity in this puzzle. Do me, this grouping doesn't make the slightest bit of sense. I simply don't know the logic between the grouped cells. Hopefully, someone can help me understand this logic. Thank you for your help.

Digit Forcing Chain
Type 2.
Whether B3 is 8 or not the chains imply C2 cannot be 3
-8[B3]+8[C3]-8[C5]+3{C5|C1}-3[C2]
+8[B3]-8[C3]+3{C3|A3}-3[C2]

Scanraid says:

Code: Select all
`36 |     7    359    1 |   369     8 3569 ||      5 1379 378 |   389      6    4 |  1239  1239  239 ||     39   16 368 |  3589    389    2 |     4 13569    7 |+-----------------+-------------------+------------------+|  34789 3789   2 |   389 134789    6 |     5  1349  349 ||      6 3579 347 |   359  13479 3579 |  1239 12349    8 ||   3489 3589   1 |     2   3489  359 |     7  3469 3469 |+-----------------+-------------------+------------------+|      1  378   9 |     6     37  357 |   238  2345  234 ||    378 3678   5 |     4      2  379 |  3689   369    1 ||     34    2 346 |     1     59    8 |   369     7 3569 |+-----------------+-------------------+--`
Glenn100

Posts: 6
Joined: 29 October 2013

### Re: Help With Grouping Digital Forcing Chains

_

Assuming the following contains the first two missing digits from your grid. The Scanraid logic is as follows:

Code: Select all
` +--------------------------------------------------------------------------------+ |  2       4       36      |  7       359     1       |  369     8       3569    | |  5       1379    378     |  389     6       4       |  1239    1239    239     | |  39      16      368     |  3589    389     2       |  4       13569   7       | |--------------------------+--------------------------+--------------------------| |  34789   3789    2       |  389     134789  6       |  5       1349    349     | |  6       3579    347     |  359     13479   3579    |  1239    12349   8       | |  3489    3589    1       |  2       3489    359     |  7       3469    3469    | |--------------------------+--------------------------+--------------------------| |  1       378     9       |  6       37      357     |  238     2345    234     | |  378     3678    5       |  4       2       379     |  3689    369     1       | |  34      2       346     |  1       59      8       |  369     7       3569    | +--------------------------------------------------------------------------------+ # 126 eliminations remain r2c3<>8  r3c3=8   r3c5<>8  r3c15=39  r3c2<>3 r2c3=8   r3c3<>8           r13c3=36  r3c2<>3`

Scanraid (apparently) fails to include the second digit for the pairs that I listed above.

Note: each stream of the forcing chain could be shortened and have the same result.

Code: Select all
`r3c3=8   r3c5<>8  r3c15=39  r3c2<>3r3c3<>8           r13c3=36  r3c2<>3`

What confuses me is that r3c2 (C2) does not contain a "3" in your grid !!!
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Help With Grouping Digital Forcing Chains

This Sudoku does have a 3 in r3c2! When I ran this through on Scanraid there is a 3r3c2 showing but when I emailed this to Super Sudoku, the 3 was not showing since this was the deleted number. Just the way Scanraid does things. Yes, you are correct there certainly should have been a 3 in r3c2. Does this make any difference in your reply? I do appreciate your reply. An interesting aspect about this puzzle was that even though it was rated 1227, I ran it through Scanraid solely with only Digital Forcing Chains selected along with the basic stuff which must run. The Digital Forcing Chains is really a powerful algorithm.
Glenn100

Posts: 6
Joined: 29 October 2013

### Re: Help With Grouping Digital Forcing Chains

Glenn100 wrote:This Sudoku does have a 3 in r3c2! When I ran this through on Scanraid there is a 3r3c2 showing but when I emailed this to Super Sudoku, the 3 was not showing since this was the deleted number. Just the way Scanraid does things. Yes, you are correct there certainly should have been a 3 in r3c2. Does this make any difference in your reply? I do appreciate your reply. An interesting aspect about this puzzle was that even though it was rated 1227, I ran it through Scanraid solely with only Digital Forcing Chains selected along with the basic stuff which must run. The Digital Forcing Chains is really a powerful algorithm.

No.

Forcing Chains are very powerful. However, many people don't use/support them. Instead, the preference is to use an AIC.

Code: Select all
` after basics and an X-Wing +--------------------------------------------------------------------------------+ |  2       4       36      |  7       359     1       |  369     8       3569    | |  5       1379    378     |  389     6       4       |  1239    1239    239     | |  39      1369    368     |  3589    389     2       |  4       13569   7       | |--------------------------+--------------------------+--------------------------| |  34789   3789    2       |  389     134789  6       |  5       1349    349     | |  6       3579    347     |  359     13479   3579    |  1239    12349   8       | |  3489    3589    1       |  2       3489    359     |  7       3469    3469    | |--------------------------+--------------------------+--------------------------| |  1       378     9       |  6       37      357     |  238     2345    234     | |  378     3678    5       |  4       2       379     |  3689    369     1       | |  34      2       346     |  1       359     8       |  369     7       3569    | +--------------------------------------------------------------------------------+ # 129 eliminations remain AIC w/2x ALS: (1=369)r1c3,r3c12 - (6=389)r3c135  =>  r3c2<>39`

The AIC can be viewed as a forcing chain where one stream is obvious and doesn't need to be explicitly listed.

Forcing chain perspective:

Code: Select all
` r3c2= 1                                       =>  r3c2<>39   (obvious stream) r3c2<>1  r1c3,r3c12=369  r3c3<>6  r3c135=389  =>  r3c2<>39`

In order to keep everyone from jumping on me all at once, I will specify that the AIC definition does not use a forcing chain perspective.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006