The New Sudoku Players' Forum

by **ArkieTech** » Fri Jul 10, 2015 11:06 pm

Code: Select all: *-----------* |...|...|..8| |95.|6..|...| |..3|.1.|96.| |---+---+---| |8.4|.2.|...| |..5|9.7|6..| |...|.3.|8.1| |---+---+---| |.82|.9.|1..| |...|..4|.29| |4..|...|...| *-----------*

Play/Print this puzzle online

by **Leren** » Sat Jul 11, 2015 12:00 am

Code: Select all: *--------------------------------------------------------------------------------* | 1 267 67 |a2357 A457 9 | 24 b357a 8 | | 9 5 8 | 6 Cd4-7e 23 | 24 1 c37 | | 27 4 3 | 257 1 8 | 9 6 57 | |--------------------------+--------------------------+--------------------------| | 8 679 4 | 15 2 156 | 57 3579 357 | | 3 1 5 | 9 8 7 | 6 4 2 | | 27 2679 679 | 4 3 56 | 8 579 1 | |--------------------------+--------------------------+--------------------------| | 6 8 2 | 357c 9 35c | 1 57b 4 | | 5 37 1 | 8 6 4 | 37 2 9 | | 4 379 79 | 12 B57d 12 | 357 8 6 | *--------------------------------------------------------------------------------* Kraken Row 1 Digit 5 : 5 r1c4 - 3 r1c4 = r1c8 - (3=7) r2c9 - 7 r2c5; 5 r1c5 - (5=7) r9c5 - 7 r2c5; 5 r1c8 - r7c8 = r7c46 - (5=7)r9c5 - 7 r2c5; => - 7 r2c5; stte

Leren

by **SteveG48** » Sat Jul 11, 2015 1:00 am

Code: Select all: *------------------------------------------------------------* | 1 267 67 | 2357 457 9 | 24 357 8 | | 9 5 8 | 6 d47 d23 |d24 1 37 | | 27 4 3 |e257 1 8 | 9 6 f57 | *-------------------+-------------------+--------------------| | 8 679 4 |a15 2 a156 | 7-5 379-5 g357 | | 3 1 5 | 9 8 7 | 6 4 2 | | 27 2679 679 | 4 3 b56 | 8 579 1 | *-------------------+-------------------+--------------------| | 6 8 2 | 357 9 c35 | 1 57 4 | | 5 37 1 | 8 6 4 | 37 2 9 | | 4 379 79 | 12 57 12 | 357 8 6 | *------------------------------------------------------------*

5r4c46 = r6c6 - (5=3)r7c6 - (3=427)r2c567 - (27=5)r3c4 - r3c9 = 5r4c9 => -5 r4c78 ; stte

by **pjb** » Sat Jul 11, 2015 3:22 am

Code: Select all: 1 267 67 |d2357 e457 9 | 24 357 8 9 5 8 | 6 47 23 | 24 1 37 27 4 3 | 257 1 8 | 9 6 57 ------------------------+----------------------+--------------------- 8 679 4 | 15 2 156 | 57 3579 357 3 1 5 | 9 8 7 | 6 4 2 27 2679 679 | 4 3 56 | 8 579 1 ------------------------+----------------------+--------------------- 6 8 2 |c357 9 35 | 1 b57 4 5 37 1 | 8 6 4 | 37 2 9 4 379 79 | 12 7-5 12 |a357 8 6 (5)r9c7 = (5-7)r7c8 = (7-3)r7c4 = (3-5)r1c4 = r1c5 => -5 r9c5; stte \ r1c8

Phil

by **Sudtyro2** » Sat Jul 11, 2015 3:51 pm

Code: Select all: *------------------------------------------------------------* | 1 267 67 | 2357 457 9 | 24 d357 8 | | 9 5 8 | 6 47 a23 | 24 1 ab37 | | 27 4 3 |c257 1 8 | 9 6 b57 | *-------------------+-------------------+--------------------| | 8 679 4 | 15 2 156 | 57 3579 357 | | 3 1 5 | 9 8 7 | 6 4 2 | | 27 2679 679 | 4 3 56 | 8 579 1 | *-------------------+-------------------+--------------------| | 6 8 2 | 35-7 9 35 | 1 57 4 | | 5 37 1 | 8 6 4 | 37 2 9 | | 4 379 79 | 12 57 12 | 357 8 6 | *------------------------------------------------------------*

The above grid is suitable for the use of MJ's CoALS rule on overlapping ALS a(237)r2c69 and b(357)r23c9. Digits in the overlap cell are the 3s and 7s. Digits in the non-overlap cells are the 2 and the 5, and both can see cell c(257)r3c4.

The CoALS rule says that there is a strong link between (all occurrences of) the AND'd digits in the overlap cell and the AND'd digits in the non-overlap cells. So, along with the cell marked c, one can form the following chain segment.

Code: Select all: [ab(73=25)r2c69,r23c9 – c(2|5=7)r3c4] <=> [7r23c9 = 7r3c4]

Either bracketed term can then be applied to Kraken cell d(357)r1c8 for an easy elimination.

Code: Select all: 7r1c8 - [7r23c9 = 7r3c4] – 7r7c4; stte || / 3r1c8 – r1c4 = r7c4 ----- || / 5r1c8 – (5=7)r7c8 ----

SteveC

by **daj95376** » Sat Jul 11, 2015 11:40 pm

Sudtyro2 wrote:
Code: Select all
*------------------------------------------------------------* | 1 267 67 | 2357 457 9 | 24 d357 8 | | 9 5 8 | 6 47 a23 | 24 1 ab37 | | 27 4 3 |c257 1 8 | 9 6 b57 | *-------------------+-------------------+--------------------| | 8 679 4 | 15 2 156 | 57 3579 357 | | 3 1 5 | 9 8 7 | 6 4 2 | | 27 2679 679 | 4 3 56 | 8 579 1 | *-------------------+-------------------+--------------------| | 6 8 2 | 35-7 9 35 | 1 57 4 | | 5 37 1 | 8 6 4 | 37 2 9 | | 4 379 79 | 12 57 12 | 357 8 6 | *------------------------------------------------------------*

The above grid is suitable for the use of MJ's CoALS rule on overlapping ALS a(237)r2c69 and b(357)r23c9. Digits in the overlap cell are the 3s and 7s. Digits in the non-overlap cells are the 2 and the 5, and both can see cell c(257)r3c4.

The CoALS rule says that there is a strong link between (all occurrences of) the AND'd digits in the overlap cell and the AND'd digits in the non-overlap cells. So, along with the cell marked c, one can form the following chain segment.
Code: Select all
[ab(73=25)r2c69,r23c9 – c(2|5=7)r3c4] <=> [7r23c9 = 7r3c4]
Either bracketed term can then be applied to Kraken cell d(357)r1c8 for an easy elimination.

Code: Select all
7r1c8 - [7r23c9 = 7r3c4] – 7r7c4; stte || / 3r1c8 – r1c4 = r7c4 ----- || / 5r1c8 – (5=7)r7c8 ----

Whew!!! That's some impressive footwork just so you can bypass:

Code: Select all: 7r1c8 - 7r7c8 = 7r7c4

_

by **Sudtyro2** » Sun Jul 12, 2015 12:08 am

daj95376 wrote: Whew!!! That's some impressive footwork just so you can bypass:
Code: Select all
7r1c8 - 7r7c8 = 7r7c4

Roger that! I needed to do a "sidestep" around that initial false premise.

SteveC

by **daj95376** » Sun Jul 12, 2015 7:08 am

Sudtyro2 wrote:Roger that! I needed to do a "sidestep" around that initial false premise.

Yes. That's what's been bothering me lately about Kraken/network forcing chains. (N-1) of N premises are false ... but ... they must all agree on an elimination. I always accepted this constraint as acceptable. Now, it's starting to bother me when it's obvious that one (or more) premise is false.

In this case, I noticed that the premise for the CoALS failed to hold water:

Code: Select all: CoALS ************************************** (7=3 )r2c9 - (3=2*)r2c6 \ (7=5*)r3c9 - *(25=7)r3c4

Leads to:

Code: Select all: CoALS plus ************************************** *************** (7=3 )r2c9 - (3=2*)r2c6 \ (7=5*)r3c9 - *(25=7)r3c4 - 7r2c5 = 7r2c9 => [7r23c9 = 7r2c9]

Or, add two cells in [r2] and rewrite to get "7r2c9 = 7r3c9":

Code: Select all: (7=3)r2c9 - (3=2*)r2c6 - (2=4)r2c7 - (4=7*)r2c5 - *(27=5)r3c4 - (5=7)r3c9 => -7 r1c8,r4c9

_

by **JC Van Hay** » Sun Jul 12, 2015 8:13 am

Code: Select all: +---------------+------------------+------------------+ | 1 267 67 | 257-3 457 9 | 24 (357) 8 | | 9 5 8 | 6 47 (23) | 24 1 37 | | 27 4 3 | (257) 1 8 | 9 6 (57) | +---------------+------------------+------------------+ | 8 679 4 | 15 2 156 | 57 3579 357 | | 3 1 5 | 9 8 7 | 6 4 2 | | 27 2679 679 | 4 3 56 | 8 579 1 | +---------------+------------------+------------------+ | 6 8 2 | (357) 9 35 | 1 (57) 4 | | 5 37 1 | 8 6 4 | 37 2 9 | | 4 379 79 | 12 57 12 | 357 8 6 | +---------------+------------------+------------------+

Broken Wings : (57)r1c8,r3c49,r7c48=*[3r1c8,3r7c4==*2r3c4 - (2=3)r2c6] :=> -3r1c4; stte

edit : rewritten chain after eleven's comment.

by **Sudtyro2** » Mon Jul 13, 2015 7:01 pm

daj95376 wrote:... I noticed that the premise for the CoALS failed to hold water:
Code: Select all
CoALS ************************************** (7=3 )r2c9 - (3=2*)r2c6 \ (7=5*)r3c9 - *(25=7)r3c4

Leads to:
Code: Select all
CoALS plus ************************************** *************** (7=3 )r2c9 - (3=2*)r2c6 \ (7=5*)r3c9 - *(25=7)r3c4 - 7r2c5 = 7r2c9 => [7r23c9 = 7r2c9]

I assume that [7r23c9 = 7r2c9] is the problem area here, because it looks like a direct contradiction. However, a discontinuous AIC loop with strong-strong inference is also a contradiction because it looks like a=b–c...d–e=a => [a=a], which also places a.

Edit: The assumptions in this paragraph are incorrect, as noted by daj95376 in his subsequent posting.
IOW, suppose one views the CoALS plus network above as two converging chains having a common end point. Then, inspection shows that the upper chain's start/end points imply [7r2c9 = 7r2c9], which therefore places 7r2c9. Similarly, the lower chain's start/end points imply [7r3c9 = 7r2c9]. Both scenarios have the common eliminations, -7r1c8,r4c9. And, the placement of 7r2c9 is also the correct solution.

It (hopefully) seems proper to view the CoALS plus network (and its implication) in this manner.

SteveC

by **daj95376** » Mon Jul 13, 2015 9:01 pm

Sudtyro2 wrote:I assume that [7r23c9 = 7r2c9] is the problem area here, because it looks like a direct contradiction. However, a discontinuous AIC loop with strong-strong inference is also a contradiction because it looks like a=b–c...d–e=a => [a=a], which also places a.

My original notes, which are now gone, indicated that there were several ways to easily convert your network stream

Code: Select all: 7r1c8 - [ 7r23c9 = 7r3c4 ] - 7r7c4

into a discontinuous loop

Code: Select all: 7r1c8 - [ 7r23c9 = 7r3c4 ] - 7r7c4 = 7r7c8 - 7r1c8 -or- 7r1c8 - [ 7r23c9 = 7r3c4 ] - 7r2c5 = 7r2c9 - 7r1c8

or a contradiction

Code: Select all: 7r1c8 - (7= 3)r2c9 - (3=*2)r2c6 - (2=4)r2c7 - (4=*7)r2c5 \ - (7=*5)r3c9 - *(257=empty)r3c4 ; contradiction

IOW, suppose one views the CoALS plus network above as two converging chains having a common end point. Then, inspection shows that the upper chain's start/end points imply [7r2c9 = 7r2c9], which therefore places 7r2c9. Similarly, the lower chain's start/end points imply [7r3c9 = 7r2c9]. Both scenarios have the common eliminations, -7r1c8,r4c9. And, the placement of 7r2c9 is also the correct solution.

It (hopefully) seems proper to view the CoALS plus network (and its implication) in this manner.

Neither stream can get past "- *(25=7)r3c4" without the other. That's why I wrote "[ 7r23c9 = 7r2c9 ]" for CoALS plus.

_

by **eleven** » Mon Jul 13, 2015 9:31 pm

JC Van Hay wrote:Broken Wings : (57)r1c8,r3c49,r7c48=*[3r1c8==*2r3c4 - (2=3)r2c6] :=> -3r1c4; stte

Love it, but don't you need 3r7c4 ?

by **Sudtyro2** » Tue Jul 14, 2015 2:02 am

daj95376 wrote: Neither stream can get past "- *(25=7)r3c4" without the other. That's why I wrote "[ 7r23c9 = 7r2c9 ]" for CoALS plus.

Yes, of course that's correct!! I went right by that minor little detail. :oops:

As per usual, many thanks for the helpful examples and clarifications!!

SteveC

by **JC Van Hay** » Tue Jul 14, 2015 6:05 am

eleven wrote:
JC Van Hay wrote:Broken Wings : (57)r1c8,r3c49,r7c48=*[3r1c8==*2r3c4 - (2=3)r2c6] :=> -3r1c4; stte

Love it, but don't you need 3r7c4 ?

I forgot it

Just replace 3r1c8 by 3r1c8,r7c4 !

The New Sudoku Players' Forum

July 11, 2015

July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015

Re: July 11, 2015