## Patterns Game 51.104

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### Patterns Game 51.104

Code: Select all
` *-----------* |1..|..2|.3.| |..4|5..|6..| |.2.|.7.|..1| |---+---+---| |.5.|...|.7.| |..6|.5.|..4| |4..|...|3..| |---+---+---| |.7.|..8|2..| |2..|6..|..3| |..8|.2.|.9.| *-----------*`

Play/Print this puzzle online
dan

ArkieTech

Posts: 3355
Joined: 29 May 2006
Location: NW Arkansas USA

### Re: Patterns Game 51.104

Code: Select all
`*--------------------------------------------------------------------------------*| 1       689     579      | 489     4689    2        | 45789   3       789-5    || 3789    389     4        | 5       1389    139      | 6       28      2789     || 35689   2       359      | 3489    7       3469     | 4589    458     1        ||--------------------------+--------------------------+--------------------------|| 389     5       1239     | 123489  134689  13469    | 189     7       2689     || 3789    1389    6        | 123789  5       1379     | 189     128     4        || 4       189     1279     | 12789   1689    1679     | 3      c56-128 b25689    ||--------------------------+--------------------------+--------------------------|| 359-6   7       1359     | 1349    1349    8        | 2      d1456   a56       || 2       149     159      | 6       149     14579    | 14578   1458    3        || 356     1346    8        | 1347    2       13457    | 1457    9       7-56     |*--------------------------------------------------------------------------------*`

M Ring Type A: (5=6) r7c9 - r7c8 = (6-5) r6c8 = r6c9 loop => - 5 r19c9, - 6 r7c1, - 128 r6c8; lclste

Leren

Correction: After seeing Phil's post I realised that what I should have said was:

M Ring Type B: (6=5) r7c9 - r6c9 = (5-6) r6c8 = r7c8 loop => - 5 r1c9, - 128 r6c8, -56 r9c9, -6 r7c1; stte

Now I know why M Rings Type A have the Base cells in different Tiers and Stacks - Ya live and learn ! Corrected the PM to reflect this.

BTW there's also an M Ring type D: (5=6) r7c9 - r46c9 = (6-5) r6c8 = r6c9 loop => - 5 r1c9, - 128 r6c8, -56 r9c9; stte

Leren

PS this has been bugging me all afternoon. The M Ring Type B is a special case with only one 6 in r789c8 at r7c8 => and additional elimination - 6 r7c1 is warranted.

Adjusted post and PM to reflect this. (I think this was the source of my confusion about the M Ring type A.)

Leren
Last edited by Leren on Fri Jun 28, 2013 8:45 am, edited 2 times in total.
Leren

Posts: 3749
Joined: 03 June 2012

### Re: Patterns Game 51.104

Code: Select all
`1      689    579    | 489    4689   2      | 45789  3      5789   3789   389    4      | 5      1389   139    | 6      28     2789   35689  2      359    | 3489   7      3469   | 4589   458    1      ---------------------+----------------------+---------------------389    5      1239   | 123489 134689 13469  | 189    7      2689   3789   1389   6      | 123789 5      1379   | 189    128    4      4      189    1279   | 12789  1689   1679   | 3     A12568 a25689  ---------------------+----------------------+---------------------3569   7      1359   | 1349   1349   8      | 2     B1456 bC56     2      149    159    | 6      149    14579  | 14578  1458   3      356    1346   8      | 1347   2      13457  | 1457   9    cD567    `

A:
1: (5-6) r7c8 = r7c8 - (6=5) r7c9 - r9c9 => r9c9 <> 5
2: (5-6) r7c8 = r7c8 - r9c9 => r9c9 <> 6

B: r9c9 = 7
1: (5) r7c9 - (5=6) r8c9 - r9c9 => r9c9 <> 6
1: (5) r7c9 - r9c9 => r9c9 <> 5

Since 5 is true in r7c8 or r7c9, r9c9 = 7; stte
Phil
pjb
2014 Supporter

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Joined: 11 September 2011
Location: Sydney, Australia

### Re: Patterns Game 51.104

ANS(28=1)r25c8
(28)r25c8 => puzzle is solved
1r5c8 => puzzle is solved

Ted
[Edit: I realize I need to expand how r5c8=1 completes the puzzle, but do not have the time now; sorry]
tlanglet
2010 Supporter

Posts: 538
Joined: 29 May 2010

### Re: Patterns Game 51.104

Leren wrote:
Code: Select all
`*--------------------------------------------------------------------------------*| 1       689     579      | 489     4689    2        | 45789   3       789-5    || 3789    389     4        | 5       1389    139      | 6       28      2789     || 35689   2       359      | 3489    7       3469     | 4589    458     1        ||--------------------------+--------------------------+--------------------------|| 389     5       1239     | 123489  134689  13469    | 189     7       2689     || 3789    1389    6        | 123789  5       1379     | 189     128     4        || 4       189     1279     | 12789   1689    1679     | 3      c56-128 b25689    ||--------------------------+--------------------------+--------------------------|| 359-6   7       1359     | 1349    1349    8        | 2      d1456   a56       || 2       149     159      | 6       149     14579    | 14578   1458    3        || 356     1346    8        | 1347    2       13457    | 1457    9       7-56     |*--------------------------------------------------------------------------------*`

M Ring Type A: (5=6) r7c9 - r7c8 = (6-5) r6c8 = r6c9 loop => - 5 r19c9, - 6 r7c1, - 128 r6c8; lclste

Correction: After seeing Phil's post I realised that what I should have said was:

M Ring Type B: (6=5) r7c9 - r6c9 = (5-6) r6c8 = r7c8 loop => - 5 r1c9, - 128 r6c8, -56 r9c9, -6 r7c1; stte

Now I know why M Rings Type A have the Base cells in different Tiers and Stacks - Ya live and learn ! Corrected the PM to reflect this.

FWIW: Here's ronk's exemplars for M-Ring Type A & B

Code: Select all
`M-Ring Type A: crc_   rcr_   w/loop .  -a   .  | .  /  .  | .  .  .-b  ab  -b  |-b  b -b  |-b -b -b .  -a   .  | .  /  .  | .  .  .------------+----------+--------- .  -a   .  | .  /  .  | .  .  . /   a   /  | / ab+ /  | /  /  / .  -a   .  | .  /  .  | .  .  .------------+----------+--------- .  -a   .  | .  /  .  | .  .  . .  -a   .  | .  /  .  | .  .  . .  -a   .  | .  /  .  | .  .  .In addition, r5c5=abM-Ring Type B: BrB_   BcB_   w/loop               rBr_   cBc_   w/loop-a -a  -a | /   /   / | .  .  .-ab ab -ab| b   b   b |-b -b -b a  a   a | /  ab+  / | /  /  /----------+-----------+--------- .  .   . | .   .   . | .  .  .In addition, r3c5=ab`

For M-Wings, ronk's exemplars always generate generic chains: (b=a)AB - (a)A = (a-b)AB+ = (b)B

I'll apply the same ordering to describe his M-Rings:

Code: Select all
`M-Ring Type A: (b=a)AB  - (a)A                      cells AB ,A always in a row/column                               =                                 (a-b)AB+ = (b)B    cells AB+,B always in a row/columnM-Ring Type B: (b=a)AB  - (a)A                      cells AB ,A always in a box, but may exist in a row/column                               =                                 (a-b)AB+ = (b)B    cells AB+,B always in a box, but may exist in a row/column`

My solver first checks to see if cells exist in rows/columns, then it "trumps" any relationship where the cells exist in a box. So, it would initially see your first chain as:

Code: Select all
`           r      c           r               ==>> M-Ring Type A interpretation (5=6)r7c9 - r7c8 = (6-5)r6c8 = r6c9 - loop`

Then it would "trump" this observation with:

Code: Select all
`           B      c           B               ==>> M-Ring Type B interpretation (5=6)r7c9 - r7c8 = (6-5)r6c8 = r6c9 - loop`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Patterns Game 51.104

Code: Select all
`+-----------------+---------------------+-------------------+| 1     689  579  | 489    4689   2     | 45789 3     5789  || 3789  389  4    | 5      1389   139   | 6     28    2789  || 35689 2    359  | 3489   7      3469  | 4589  458   1     |+-----------------+---------------------+-------------------+| 389   5    1239 | 123489 134689 13469 | 189   7     2689  || 3789  1389 6    | 123789 5      1379  | 189   128   4     || 4     189  1279 | 12789  1689   1679  | 3     12568 25689 |+-----------------+---------------------+-------------------+| 3569  7    1359 | 1349   1349   8     | 2     1456  56    || 2     149  159  | 6      149    14579 | 14578 1458  3     || 356   1346 8    | 1347   2      13457 | 1457  9     567   |+-----------------+---------------------+-------------------+`

Play this puzzle online at the Daily Sudoku site

1) M-Wing (6=5)r7c9-r6c9=(5-6)r6c8=r7c8=>r9c9<>6
2) 5r6c9=(5-6)r8c8=r7c8-(6=5)r7c9=>r9c9<>5=7
Marty R.

Posts: 1508
Joined: 23 October 2012
Location: Rochester, New York, USA

### Re: Patterns Game 51.104

[Edit: I realize I need to expand how r5c8=1 completes the puzzle, but do not have the time now; sorry]

Ted, I certainly could be wrong, but four times using Draw/Play, r5c8=1=>invalidity. That cell ends up =2 in the completed puzzle.
Marty R.

Posts: 1508
Joined: 23 October 2012
Location: Rochester, New York, USA

### Re: Patterns Game 51.104

Marty R. wrote:
[Edit: I realize I need to expand how r5c8=1 completes the puzzle, but do not have the time now; sorry]

Ted, I certainly could be wrong, but four times using Draw/Play, r5c8=1=>invalidity. That cell ends up =2 in the completed puzzle.

Marty, I agree that r5c8<>1 but it still solves the puzzle.

Code: Select all
`1r5c8-(1=89)r45c7-(89)r1*3c7        =(45)r3c78-(8945=7)r1*c7 => basics completes the puzzle.                 \                  /                  -8r8c7=r8c8-8r3c8`

So if (28)r25c8 is true => puzzle is solved
and if r5c8=1 is true => puzzle is solved

One of these conditions must be true; either r5c8=28 or r5c8=1. This is just like a simple xy-wing where only one pincer is true since either "x" or "y" in the pivot cell can be true.

Ted
tlanglet
2010 Supporter

Posts: 538
Joined: 29 May 2010

### Re: Patterns Game 51.104

daj 95376 Wrote : Here's ronk's exemplars for M-Ring Type A & B

Hi Danny, the way I've gotten around this M Ring type A or Type B interpretation issue is to include a special case of an M Ring Type B. An M Ring type AB ?

Code: Select all
`-a -a  -a | /   /   / | .  .  .-ab ab -ab| b   b   b |-b -b -b /  a   / | /  ab+  / | /  /  /----------+-----------+---------.  -a   . | .  /   .  | .  .  ..  -a   . | .  /   .  | .  .  ..  -a   . | .  /   .  | .  .  .----------+-----------+---------.  -a   . | .  /   .  | .  .  ..  -a   . | .  /   .  | .  .  ..  -a   . | .  /   .  | .  .  .`

This is the same as an M Ring type B except that there happen to be no a's in r3c13 (in the exemplar diagram) so there
is a Strong link on a in Row 3 (as opposed to a grouped Strong link for the general case of an M Ring type B). That way I pick up
both the -ab eliminations in r2c13 ( -56 r9c9 in the puzzle - which solves the puzzle with an stte end) and also the -a's in r456789c2
( - 6 r7c1 in the puzzle - which is just plain satisfying).

If you can have an M Wing Type 2C which combines elements of M Wings Type 2A and 2B then I can't see why you can't have an M Ring Type AB
which combines elements of M Rings Types A and B. Well, that's my story and I sticking to it

Leren
Leren

Posts: 3749
Joined: 03 June 2012