The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|.2.|48.|
 |..5|.6.|..2|
 |...|93.|7..|
 |---+---+---|
 |...|...|1.8|
 |.54|...|63.|
 |7.3|...|...|
 |---+---+---|
 |..9|.42|...|
 |4..|.9.|5..|
 |.87|.1.|...|
 *-----------*


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[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 39      379     6        | 1       2       57       | 4       8       35       |
| 13      47      5        | 478     6       478      | 39      19      2        |
| 12      24      8        | 9       3       45       | 7      d156    c16-5     |
|--------------------------+--------------------------+--------------------------|
| 69      69      2        | 34      5       34       | 1       7       8        |
| 8       5       4        | 2       7       1        | 6       3       9        |
| 7       1       3        | 6       8       9        | 2       45      45       |
|--------------------------+--------------------------+--------------------------|
| 356     36      9        | 357     4       2        | 8      a16     b1367     |
| 4       236     1        | 378     9       3678     | 5       2-6     367      |
| 2356    8       7        | 35      1       36       | 39      249-6   346      |
*--------------------------------------------------------------------------------*

M Ring: (6=1) r7c8 - r7c9 =(1-6) r3c9 = r3c8 - r7c8 Loop => r89c8 <6>, r3c9 <5>

Leren

[storm_norm22]

Code: Select all

+------------------+---------------+-------------------+
| 39      379    6 | 1    2  57    | 4     8      35   |
| (13)    47     5 | 478  6  478   | 9(3)  19     2    |
| (12)    24     8 | 9    3  45    | 7     156    156  |
+------------------+---------------+-------------------+
| 69      69     2 | 34   5  34    | 1     7      8    |
| 8       5      4 | 2    7  1     | 6     3      9    |
| 7       1      3 | 6    8  9     | 2     45     45   |
+------------------+---------------+-------------------+
| 356     36     9 | 357  4  2     | 8     16     1367 |
| 4       36(2)  1 | 378  9  378-6 | 5     (26)   367  |
| 356(2)  8      7 | 35   1  (36)  | 9(3)  249-6  34-6 |
+------------------+---------------+-------------------+

(3=6)r9c6 - (3)r9c7 = (3)r2c7 - (3=1)r2c1 - (2=1)r3c1 - (2)r9c1 = (2)r8c2 - (2=6)r8c8; r8c6 <> 6 and r9c89 <> 6

[ArkieTech]

Code: Select all

*--------------------------------------------------------------------------------*
| 39      379     6        | 1       2       57       | 4       8       35       |
| 13      47      5        | 478     6       478      | 39      19      2        |
| 12      24      8        | 9       3       45       | 7      d156    c16-5     |
|--------------------------+--------------------------+--------------------------|
| 69      69      2        | 34      5       34       | 1       7       8        |
| 8       5       4        | 2       7       1        | 6       3       9        |
| 7       1       3        | 6       8       9        | 2       45      45       |
|--------------------------+--------------------------+--------------------------|
| 356     36      9        | 357     4       2        | 8      a16     b1367     |
| 4       236     1        | 378     9       3678     | 5       2-6     367      |
| 2356    8       7        | 35      1       36       | 39      249-6   346      |
*--------------------------------------------------------------------------------*

M Ring: (6=1) r7c8 - r7c9 =(1-6) r3c9 = r3c8 - r7c8 Loop => r89c8 <6>, r3c9 <5>

Leren

I have always called this a "loop" or "continous loop". What is an m-ring?

[tlanglet]

I started this puzzle by noticing a couple of BUG-Lite patterns including this one step solution

BUG-Lite+4(456)r369c89[6r9c16=(5-4)r3c6]=(4-2)r3c2=r8c2-(2=6)r8c8 => r9c89<>6

Ted

[Marty R.]

Nice Ted. I looked at a bunch of those URs/BUG lites and didn't see anything I could do.

Code: Select all

+------------+------------+--------------+
| 39   379 6 | 1   2 57   | 4  8    35   |
| 13   47  5 | 478 6 478  | 39 19   2    |
| 12   24  8 | 9   3 45   | 7  156  156  |
+------------+------------+--------------+
| 69   69  2 | 34  5 34   | 1  7    8    |
| 8    5   4 | 2   7 1    | 6  3    9    |
| 7    1   3 | 6   8 9    | 2  45   45   |
+------------+------------+--------------+
| 356  36  9 | 357 4 2    | 8  16   1367 |
| 4    236 1 | 378 9 3678 | 5  26   367  |
| 2356 8   7 | 35  1 36   | 39 2469 346  |
+------------+------------+--------------+


Play this puzzle online at the Daily Sudoku site

Some kind of nameless (to me) loop.

(6=2)r8c8-r8c2=r9c1-(2=1)r3c1-r3c89=r2c8-(1=6)r3c8=>r3c8<>16

[daj95376]

I've lost count of the number of times my solver has found this particular UR pattern in puzzles.

Code: Select all

--- UR+3U/2SL: the strong links are disjoint with different labels => "a" can be removed from "abY"

 ab-----abX
     a

     b
abY-----abZ


Code: Select all

 after basics
 +--------------------------------------------------------------+
 |  39    379   6     |  1     2     57    |  4     8     35    |
 |  13    47    5     |  478   6     478   |  39    19    2     |
 |  12    24    8     |  9     3     45    |  7    *16+5 *16+5  | <- SL on "6"
 |--------------------+--------------------+--------------------|
 |  69    69    2     |  34    5     34    |  1     7     8     |
 |  8     5     4     |  2     7     1     |  6     3     9     |
 |  7     1     3     |  6     8     9     |  2     45    45    |
 |--------------------+--------------------+--------------------|
 |  356   36    9     |  357   4     2     |  8    *16   *16+37 | <- SL on "1"
 |  4     236   1     |  378   9     3678  |  5     26    367   |
 |  2356  8     7     |  35    1     36    |  39    2469  346   |
 +--------------------------------------------------------------+
 # 56 eliminations remain

 r37c89  <16> UR+3U/2SL                             r3c8<>1

 (2=4)r3c2 - (4=5)r3c6 - (5=6)r3c8 - (6=2)r8c8  =>  r8c2<>2


[Leren]

ArkieTech Wrote : What is an m-ring?

Some M Wing and M Ring discussion has been removed from this forum

The following is an external link that retains some of this information.

https://www.speedsudoku.com/forum/viewtopic.php?f=58&t=695

The M Ring I found in this puzzle is a Type A as described in this link.

Leren

[Luke]

I started this puzzle by noticing a couple of BUG-Lite patterns including this one step solution

BUG-Lite+4(456)r369c89[6r9c16=(5-4)r3c6]=(4-2)r3c2=r8c2-(2=6)r8c8 => r9c89<>6

Nice, Ted. A DP with only two outs is always fun to look at. The (369) BUG-Lite in chute 1 has only two as well, but not as much fun if one is looking for a one-stepper.

[pjb]

Starting from Leren's grid, another one step solution uses the ALS XZ technique:

ALS 1 of 13569 at r1c9, r2c78, r3c8
ALS 2 of 16 at r7c8
X value 1, Z value 6
eliminates 6 from r89c8

pjb

[storm_norm22]

the m-ring is simply an m-wing in which the first and last nodes reside in the same box, same row or same column.

when this happens all eliminations happen along the houses that contain the weak links. hence why there are more eliminations in the chain.

[ArkieTech]

the m-ring is simply an m-wing in which the first and last nodes reside in the same box, same row or same column.

when this happens all eliminations happen along the houses that contain the weak links. hence why there are more eliminations in the chain.

Thanks Norm,

Are all rings loops? I assume all loops are not rings.

[pjb]

I might be a bit old fashioned, but isn't Leren's M-ring also called a 'nice' loop?
pjb

[Leren]

daj 95376 wrote: r37c89 <16> UR+3U/2SL r3c8<>1

There's also a third SL (on 1 in column 9) in this UR which also => r7c9 <6>

Also, in your diagram woudn't it be better to write it as

Code: Select all

 ab-----aX
     a

     b
abY-----bZ

ie b doesn't have to be in the top right hand cell and a doesn't have to be in the bottom right hand cell

Leren

[storm_norm22]

I am not sure how many patterns get the name "ring" but regardless of whether the pattern is called a ring, all loops perform exactly the same. the issue isn't whether the pattern gets a name... the issue is recognizing why a pattern forms a loop. its something that can be missed and/or misunderstood.

for example. the discussion in the daily forums about the "half m-wing"... Ravel's example... this pattern is a m-wing that starts and ends in the same box which forms a loop... and in that example there is another elimination which has not been pointed out. this is a good example of how all of the chain's logic is sometimes overlooked in our mind's eye.