## Robert's puzzles 2020-09-22

Post puzzles for others to solve here.

### Robert's puzzles 2020-09-22

Hi all,
I propose you this puzzle.
Good resolution
Robert
.2.5.9.7.....4.9.2..93.....93...1..62.......71..8...94.....576.6...1.....4.6.3.5.
puzzle: Show

resolution: Show
Note the X-wing 2C4-2C8 which allows the elimination of several 2, but which is not used here. .
P'(7r8c46) : (-7r8c46)->75r8c23->9r7c2->9r9c5 => r9c5≠7 => r8c23≠7.

P'(8r4c8) : (-8r4c8)->2r4c8->7r4c4->2r8c4->(7r8c6 and 89r79c5->6r1c5)->8r2c6->3r2c8 => -8r2c8 => r2c8=3, r5c8=1.

P'(8r1c9) : (-8r1c9)->1r1c9->(1r3c2 and 1r9c7)->1r7c3->2r7c5->2r4c4->8r4c8 => -8r3c8 => r3c8=4. stte.

Last edited by Mauriès Robert on Wed Sep 23, 2020 6:32 am, edited 7 times in total.
Mauriès Robert

Posts: 345
Joined: 07 November 2019
Location: France

### Re: Robert's puzzles 2020-09-22

Hi Robert,

Disclaimer: I didn't have time to start solving a multi-stepper from scratch, so I cheated and looked at your eliminations (not the actual moves). They seemed pretty efficient, so I built my own moves around them. I haven't checked how close they are to yours, but I guess they can't be very far off.

Step 1. AIC: Show
Code: Select all
`.-------------------.--------------------.-------------------.| 348  2     1368   |  5    68      9    | 13468  7     138  || 5    678   3678   |  1    4       678  | 9      38    2    || 478  1678  9      |  3    2678    2678 | 1468   148   5    |:-------------------+--------------------+-------------------:| 9    3     4      |  27   257     1    | 258    28    6    || 2    568   568    |  9    356     4    | 135    13    7    || 1    567   567    |  8    2356    26   | 235    9     4    |:-------------------+--------------------+-------------------:| 38  b189   1238   |  4   c289     5    | 7      6     1389 || 6   b5789  b23578 | a27   1      a278  | 2348   2348  389  || 78   4     1278   |  6   d289-7   3    | 128    5     189  |'-------------------'--------------------'-------------------'`

(7)r8c46 = (759)b7p652 - r7c5 = (9)r9c5 => -7 r9c5

- 4x4 PM: Show
Code: Select all
` 9r9c5  9r7c5        9r7c2 9r8c2              5r8c2 5r8c3 7r8c46       7r8c2 7r8c3=========================-7r9c5`

(I guess that would translate to a t-whip in Denis' system.)

Step 2. AIC (with nesting): Show
Code: Select all
`.-----------------.---------------------.-------------------.| 348  2     1368 |  5     68      9    | 13468  7     138  || 5    678   3678 |  1     4     ab678  | 9      3-8   2    || 478  1678  9    |  3   ef2678   d2678 | 1468   148   5    |:-----------------+---------------------+-------------------:| 9    3     4    | g27   g257     1    | 258   g28    6    || 2    568   568  |  9     356     4    | 135    13    7    || 1    567   567  |  8     2356   c26   | 235    9     4    |:-----------------+---------------------+-------------------:| 38   189   1238 |  4     289     5    | 7      6     1389 || 6    589   2358 |  27    1       278  | 2348   2348  389  || 78   4     1278 |  6     289     3    | 128    5     189  |'-----------------'---------------------'-------------------'`

(8)r2c6 = [(7=6)r2c6 - (6=2)r6c6 - r3c6 = (2)r3c5] - 7r3c5 = (728)r4c548 => -8 r2c8

- 6x6 TM: Show
Code: Select all
` 8r4c8 2r4c8       2r4c4 7r4c4             7r4c5 7r3c5                   2r3c5 2r3c6                         2r6c6 6r6c6 8r2c6             7r2c6       6r2c6====================================-8r2c8`

(I guess that would translate to a t-whip.)

Step 3. AIC (with nesting): Show
Code: Select all
`.-----------------.-----------------.---------------------.| 348  2     1368 |  5   68    9    |   1468    7    18   || 5    678   678  |  1   4     678  |   9       3    2    || 478  1678  9    |  3   2678  2678 |   1468   i4-8  5    |:-----------------+-----------------+---------------------:| 9    3     4    | b27  257   1    |  f258   ae28   6    || 2    568   568  |  9   356   4    |   35      1    7    || 1    567   567  |  8   2356  26   |   235     9    4    |:-----------------+-----------------+---------------------:| 38   189   1238 |  4   289   5    |   7       6    1389 || 6    59    35   | c27  1     278  | dg248    h248  39   || 78   4     1278 |  6   289   3    |   128     5    189  |'-----------------'-----------------'---------------------'`

(8=2)r4c8 - r4c4 = r8c4 - 2r8c7 = [(8)r4c8 = r4c7 - (8=4)r8c7 - r8c8 = (4)r3c8] => -8 r3c8

- 5x5 TM: Show
Code: Select all
` 8r4c8 2r4c8       2r4c4 2r8c4 8r4c8             8r4c7             2r8c7 8r8c7 4r8c7 4r3c8                   4r8c8==============================-8r3c8; stte`

(I guess that would translate to a braid.)

--
I actually found steps 2 and 3 together, but it gets pretty ugly if they're written as a single move.

Step 2. Memory chain (with a subchain): Show
Code: Select all
`.-----------------.--------------------.---------------------.| 348  2     1368 |   5    68     9    |  13468   7     138  || 5    678   3678 |   1    4     f678  |  9      g3-8   2    || 478  1678  9    |   3   e2678  e2678 |  1468   m14-8  5    |:-----------------+--------------------+---------------------:| 9    3     4    | bc27  d257    1    | a258*   a28    6    || 2    568   568  |   9    356    4    | i135    h13    7    || 1    567   567  |   8    2356  e26   | i235     9     4    |:-----------------+--------------------+---------------------:| 38   189   1238 |   4    289    5    |  7       6     1389 || 6    589   2358 |  c27^  1      278  | j2348   k2348  389  || 78   4     1278 |   6    289    3    |  128     5     189  |'-----------------'--------------------'---------------------'`

(8)r4c8 = (8*,2)r4c78 - r4c4 = (2^,7)r84c4 - r4c5 = (726)r3c5,r36c6 - (2|6=8)r2c6@ - (8=3)r2c8 - r5c8 = r56c7 - (3|*8|^2=4)r8c7 - r8c8 = (4)r3c8 => -8 r23c8; stte

- 12x12 TM: Show
Code: Select all
` 8r4c8 ..... 2r4c8             2r4c4 7r4c4                   7r4c5 7r3c5                         2r3c5 2r3c6                               2r6c6 6r6c6                         7r2c6 ..... 6r2c6 8r2c6                                           8r2c8 3r2c8                                                 3r5c8 3r56c7             2r4c4 .......................................... 2r8c4 8r4c8 ............................................................ 8r4c7                                                       3r8c7  2r8c7 8r8c7 4r8c7 8r2c6,4r3c8 ........... 7r2c6 ..... 6r2c6 .............................. 4r8c8=============================================================================== -8r2c8,8r3c8`

(There's probably no direct translation to Denis' system, but if there were, it would be a braid.)

--
PS. To avoid boring copycatting like this, you probably shouldn't post your own resolution right away
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2568
Joined: 22 May 2017

### Re: Robert's puzzles 2020-09-22

Even though I activated whips, only simple short reversible chains (bivalue-chains and z-chains) are needed.

Code: Select all
`(solve ".2.5.9.7.....4.9.2..93.....93...1..62.......71..8...94.....576.6...1.....4.6.3.5.")**************************************************************************************************  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin***  Using CLIPS 6.32-r770***********************************************************************************************hidden-single-in-a-row ==> r7c4 = 4naked-single ==> r5c4 = 9hidden-single-in-a-block ==> r5c6 = 4hidden-single-in-a-block ==> r4c3 = 4hidden-single-in-a-column ==> r3c9 = 5hidden-single-in-a-column ==> r2c1 = 5hidden-single-in-a-column ==> r2c4 = 1158 candidates, 788 csp-links and 788 links. Density = 6.35%whip[1]: r4n8{c8 .} ==> r5c8 ≠ 8, r5c7 ≠ 8whip[1]: r4n7{c5 .} ==> r6c6 ≠ 7, r6c5 ≠ 7x-wing-in-columns: n2{c4 c8}{r4 r8} ==> r8c7 ≠ 2, r8c6 ≠ 2, r8c3 ≠ 2, r4c7 ≠ 2, r4c5 ≠ 2biv-chain[3]: r4n8{c7 c8} - c8n2{r4 r8} - b9n4{r8c8 r8c7} ==> r8c7 ≠ 8biv-chain[3]: r8c7{n3 n4} - r1n4{c7 c1} - c1n3{r1 r7} ==> r7c9 ≠ 3, r8c3 ≠ 3biv-chain[3]: c9n3{r1 r8} - r8c7{n3 n4} - r1n4{c7 c1} ==> r1c1 ≠ 3hidden-single-in-a-column ==> r7c1 = 3z-chain-bn[3]: b7n9{r8c2 r7c2} - b8n9{r7c5 r9c5} - b8n7{r9c5 .} ==> r8c2 ≠ 7z-chain-rc[3]: r8c6{n8 n7} - r2c6{n7 n6} - r1c5{n6 .} ==> r3c6 ≠ 8biv-chain[3]: c6n8{r8 r2} - r2c8{n8 n3} - c9n3{r1 r8} ==> r8c9 ≠ 8biv-chain[4]: r4n5{c5 c7} - b6n8{r4c7 r4c8} - b6n2{r4c8 r6c7} - r6n3{c7 c5} ==> r6c5 ≠ 5biv-chain[4]: r2c8{n8 n3} - c9n3{r1 r8} - r8c7{n3 n4} - c8n4{r8 r3} ==> r3c8 ≠ 8biv-chain[4]: r8n9{c2 c9} - c9n3{r8 r1} - r2c8{n3 n8} - c6n8{r2 r8} ==> r8c2 ≠ 8z-chain-rn[4]: r8n7{c6 c3} - r8n5{c3 c2} - r8n9{c2 c9} - r9n9{c9 .} ==> r9c5 ≠ 7whip[1]: r9n7{c3 .} ==> r8c3 ≠ 7biv-chain[3]: r8n7{c6 c4} - r4c4{n7 n2} - c6n2{r6 r3} ==> r3c6 ≠ 7naked-pairs-in-a-column: c6{r3 r6}{n2 n6} ==> r2c6 ≠ 6whip[1]: r2n6{c3 .} ==> r1c3 ≠ 6, r3c2 ≠ 6biv-chain[3]: r3n2{c6 c5} - c5n7{r3 r4} - r4c4{n7 n2} ==> r6c6 ≠ 2naked-single ==> r6c6 = 6naked-single ==> r3c6 = 2naked-pairs-in-a-block: b4{r6c2 r6c3}{n5 n7} ==> r5c3 ≠ 5, r5c2 ≠ 5whip[1]: b4n5{r6c3 .} ==> r6c7 ≠ 5biv-chain-rc[3]: r6c3{n7 n5} - r8c3{n5 n8} - r9c1{n8 n7} ==> r9c3 ≠ 7hidden-single-in-a-block ==> r9c1 = 7whip[1]: c1n8{r3 .} ==> r1c3 ≠ 8, r2c2 ≠ 8, r2c3 ≠ 8, r3c2 ≠ 8biv-chain-rc[3]: r6c7{n3 n2} - r4c8{n2 n8} - r2c8{n8 n3} ==> r5c8 ≠ 3, r1c7 ≠ 3naked-single ==> r5c8 = 1naked-single ==> r3c8 = 4naked-single ==> r3c1 = 8naked-single ==> r1c1 = 4hidden-single-in-a-column ==> r8c7 = 4biv-chain-rc[4]: r4c7{n8 n5} - r4c5{n5 n7} - r3c5{n7 n6} - r1c5{n6 n8} ==> r1c7 ≠ 8naked-pairs-in-a-block: b3{r1c7 r3c7}{n1 n6} ==> r1c9 ≠ 1whip[1]: c9n1{r9 .} ==> r9c7 ≠ 1biv-chain[3]: r9n1{c9 c3} - r1c3{n1 n3} - r1c9{n3 n8} ==> r9c9 ≠ 8biv-chain[4]: r4c8{n8 n2} - c4n2{r4 r8} - r8n7{c4 c6} - c6n8{r8 r2} ==> r2c8 ≠ 8stte`
denis_berthier
2010 Supporter

Posts: 1672
Joined: 19 June 2007
Location: Paris

### Re: Robert's puzzles 2020-09-22

Hi Space,
SpAce wrote:Disclaimer: I didn't have time to start solving a multi-stepper from scratch, so I cheated and looked at your eliminations (not the actual moves). They seemed pretty efficient, so I built my own moves around them. I haven't checked how close they are to yours, but I guess they can't be very far off.

Your resolution is equivalent to mine, and its interest lies in the fact that it is expressed with correctly written AICs and TMs, which I do not know how to do.
Cordialy
Robert
Mauriès Robert

Posts: 345
Joined: 07 November 2019
Location: France

### Re: Robert's puzzles 2020-09-22

Hi Denis,
Your SudoRules solver is set to find a resolution with the shortest strings and in this case the number of strings used is free. Is it configurable to find a resolution with a minimum number of strings whose length is free or limited?
Cordialement
Robert
Mauriès Robert

Posts: 345
Joined: 07 November 2019
Location: France

### Re: Robert's puzzles 2020-09-22

Two steps:
Code: Select all
` +-----------------------+-------------------------+------------------------+ |  348   2      1368    |    5    68       9      |  13468   7     M138    |  |  5     678    3678    |    1    4       G678    |  9      M3-8    2      |  |  478   1678   9       |    3    2678E*   2678D* |  1468    14-8   5      |  +-----------------------+-------------------------+------------------------+ |  9     3      4       |   A27   257F*    1      |  258    A28     6      |  |  2     568    568     |    9    356      4      |  135     13     7      |  |  1     567    567     |    8    2356     26     |  235     9      4      |  +-----------------------+-------------------------+------------------------+ |  38    189    1238    |    4    289      5      |  7       6     L1389   |  |  6    e589-7 e2358-7  |  Ha27B* 1      Ha278C*  | J2348   J2348  d389    |  |  78    4      1278    |    6   b2789     3      | K128     5    Lc189    |  +-----------------------+-------------------------+------------------------+`

1. (7)r8c46 = (7-9)r9c5 = r9c9 - r8c9 = (95)r8c23 => -7 r8c23
2. (8=27)r4c48 - [(7)r8c4 = (7-8)r8c6 = (8-2)r3c6 = (2-7)r3c5 = (7)r4c5] = (8)r2c6^ - (8=72)r8c46 - r8c78 = (2-1)r9c7 = r79c9 - (1=38)b3p35 => -8 r2c8^, -8 r3c8; ste
(Note: the embedded chain is tagged from B* to F*, behind the pencilmarks, the spoiler chain is tagged from G to M, skiping I)
Cenoman
Cenoman

Posts: 1517
Joined: 21 November 2016
Location: Paris, France

### Re: Robert's puzzles 2020-09-22

Mauriès Robert wrote:Hi Denis,
Your SudoRules solver is set to find a resolution with the shortest strings and in this case the number of strings used is free. Is it configurable to find a resolution with a minimum number of strings whose length is free or limited?
Cordialement
Robert

No, because such a condition is not expressible in purely logical terms.
denis_berthier
2010 Supporter

Posts: 1672
Joined: 19 June 2007
Location: Paris

### Re: Robert's puzzles 2020-09-22

Mauriès Robert wrote:Your resolution is equivalent to mine, and its interest lies in the fact that it is expressed with correctly written AICs and TMs, which I do not know how to do.

Indeed. Now that I took a look at your actual moves, it seems that our first steps are identical. The second and third take a bit different routes for the same effect:

Your step 2:

8x8 BTM: Show
Code: Select all
` 8r4c8 2r4c8       2r4c4 7r4c4             7r8c4 2r8c4                   2r7c5 9r7c5 8r7c5                    2r9c5 9r9c5 8r9c5                                8r1c5 6r1c5                   7r8c4                   7r8c6 8r2c6                               6r2c6 7r2c6================================================-8r2c8`

Note: that can be reduced to a 7x7 matrix by removing the unnecessary 7r4c4:

Code: Select all
` 8r4c8 2r4c8       2r4c4 2r8c4             2r7c5 9r7c5 8r7c5              2r9c5 9r9c5 8r9c5                          8r1c5 6r1c5             7r8c4                   7r8c6 8r2c6                         6r2c6 7r2c6==========================================-8r2c8`

It's probably easiest to read as a 6x6 TM with the folded ALS:

Code: Select all
` 8r4c8 2r4c8       2r4c4 2r8c4             2r79c5 89r79c5                    8r1c5   6r1c5             7r8c4                7r8c6 8r2c6                      6r2c6 7r2c6=======================================-8r2c8`

AIC (with nesting): Show
Code: Select all
`.-----------------.---------------------.--------------------.| 348  2     1368 |   5   e68      9    | 13468   7     138  || 5    678   3678 |   1    4     fi678  | 9       3-8   2    || 478  1678  9    |   3    2678    2678 | 1468    148   5    |:-----------------+---------------------+--------------------:| 9    3     4    |  b27   257     1    | 258    a28    6    || 2    568   568  |   9    356     4    | 135     13    7    || 1    567   567  |   8    2356    26   | 235     9     4    |:-----------------+---------------------+--------------------:| 38   189   1238 |   4   d289     5    | 7       6     1389 || 6    589   2358 | ch27   1      g278  | 2348    2348  389  || 78   4     1278 |   6   d289     3    | 128     5     189  |'-----------------'---------------------'--------------------'`

(8=2)r4c8 - r4c4 = 2r8c4 - [(2=98)r79c5 - (8=6)r1c5 - (6=7)r2c6 - r8c6 = (7)r8c4] = (8)r2c6 => -8 r2c8

That would probably translate to a braid, while mine to a whip.

Your step 3:

7x7 TM: Show
Code: Select all
` 8r1c9 1r1c9       1r1c3  1r3c2       1r79c9       1r9c7              1r7c2 1r9c3 1r7c3                          2r7c3 2r7c5                                2r8c4 2r4c4 8r4c8                                2r4c8===========================================-8r3c8 `

AIC (with nesting): Show
Code: Select all
`.-------------------.------------------.--------------------.| 348   2     b1368 |  5    68    9    |  1468   7    a18   || 5     678    678  |  1    4     678  |  9      3     2    || 478  c1678   9    |  3    2678  2678 |  1468   4-8   5    |:-------------------+------------------+--------------------:| 9     3      4    | k27   257   1    |  258   m28    6    || 2     568    568  |  9    356   4    |  35     1     7    || 1     567    567  |  8    2356  26   |  235    9     4    |:-------------------+------------------+--------------------:| 38   d189   h1238 |  4   i289   5    |  7      6    g1389 || 6     59     35   | j27   1     278  |  248    248   39   || 78    4     e1278 |  6    289   3    | f128    5    g189  |'-------------------'------------------'--------------------'`

(8=1)r1c9 - [(1)r1c3 = r3c2 - r7c2 = r9c3 - r9c7 = (1)r79c9] = (1-2)r7c3 = r7c5 - r8c4 = r4c4 - (2=8)r4c8 => -8 r3c8

That would probably translate to a braid as well, just like my third step.

(Denis is welcome to correct my assumptions, but if I've understood anything, the difference between whips and braids is trivial to see in the matrix form. For the same reason it's easy to see why braids are confluent and whips are not.)

SpAce

Posts: 2568
Joined: 22 May 2017

### Re: Robert's puzzles 2020-09-22

Hi Cenoman

Cenoman wrote:
2. (8=27)r4c48 - [(7)r8c4 = (7-8)r8c6 = (8-2)r3c6 = (2-7)r3c5 = (7)r4c5] = (8)r2c6^ - (8=72)r8c46 - r8c78 = (2-1)r9c7 = r79c9 - (1=38)b3p35 => -8 r2c8^, -8 r3c8; ste

The second step is not clear to me. My problem is to understand what is the logical motivation that allows us to discard the conclusions of the first logical chain, the one with (= (8) r3c6), which is a discontinuous nice loop and to accept vice versa the conclusions of the second, the one with ( = (8) r2c6) ^?

Paolo
Ajò Dimonios

Posts: 201
Joined: 07 November 2019

### Re: Robert's puzzles 2020-09-22

Ajò Dimonios wrote:The second step is not clear to me. My problem is to understand what is the logical motivation that allows us to discard the conclusions of the first logical chain, the one with (= (8) r3c6), which is a discontinuous nice loop and to accept vice versa the conclusions of the second, the one with ( = (8) r2c6) ^?

My step 2 is actually a kraken column written on a single line:
Kraken column (8)r238c6 => -8 r2c8^, -8 r3c8
(8)r2c6^ - (8=72)r8c46 - r8c78 = (2-1)r9c7 = r79c9 - (1=38)b3p35
(8-2)r3c6 = (2-7)r3c5 = r4c5 - (7=28)r4c48
(8-7)r8c6 = r8c4 - (7=28)r4c48

Only two AIC's are considered in my step 2:
(keeping only the endpoints) (8)r4c8 == (38)b3p35 and the sub-chain (8)r4c8 == (8)r2c6
I see no chain having 8r3c6 as an endpoint. The chain inside the brackets can't be split. It is an almost chain, as the strong link 8r8c6 = 8r3c6 is spoiled by 8r2c6, treated separately.
Cenoman
Cenoman

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Location: Paris, France

### Re: Robert's puzzles 2020-09-22

Ajò Dimonios wrote:
Cenoman wrote:
2. (8=27)r4c48 - [(7)r8c4 = (7-8)r8c6 = (8-2)r3c6 = (2-7)r3c5 = (7)r4c5] = (8)r2c6^ - (8=72)r8c46 - r8c78 = (2-1)r9c7 = r79c9 - (1=38)b3p35 => -8 r2c8^, -8 r3c8; ste

The second step is not clear to me. My problem is to understand what is the logical motivation that allows us to discard the conclusions of the first logical chain, the one with (= (8) r3c6), which is a discontinuous nice loop and to accept vice versa the conclusions of the second, the one with ( = (8) r2c6) ^?

You need to read it like this:

(8=2)r4c8 - (2=7)r4c4 - [nested AIC] = (8)r2c6
The whole nested chain is a single node in the outer AIC. It has a weak link with 7r4c4 and a strong link with 8r2c6. If you read it from left to right, 7r4c4 is assumed true and thus the nested AIC is false and 8r2c6 is true. If you read it from right to left, it's vice versa. The chain in the nested part could be written in either orientation. This would work just the same:

(8=2)r4c8 - (2=7)r4c4 - [(7)r4c5 = (7-2)r3c5 = (2-8)r3c6 = (8-7)r8c6 = (7)r8c4] = (8)r2c6
If one wants to go nuts with nested chains, adding another would get both eliminations without needing the subchain:

(8=27)r4c84 - [(7)r4c5 = (72-8)r3c56 = (87)r8c64] = 8r2c6 - [(8=72)r8c64 - r8c78 = (21)b9p739 - (1=3,8)b3p35] = (8)r1c9 => -8 r23c8
uncompressed: Show
(8=2)r4c8 - (2=7)r4c4 - [(7)r4c5 = (7-2)r3c5 = (2-8)r3c6 = (8-7)r8c6 = (7)r8c4] = (8)r2c6 - [(8=72)r8c64 - r8c78 = (2-1)r9c7 = r79c9 - (1=3)r1c9 - (3=8)r2c8] = (8)r1c9 => -8 r23c8

@Cenoman: Nice job! Much better than my horrible memory chain (I see you also replied while I was typing this.)

SpAce

Posts: 2568
Joined: 22 May 2017

### Re: Robert's puzzles 2020-09-22

Hi Paolo and SpAce,

It was "round midnight" when I posted yesterday! I felt that some more information about embedded AIC's would be useful.
SpAce did it. Thanks !

BTW is 'embedded' synonym of 'nested' ? (English isn't my native language)

I like the short writing
(8=2)r4c8 - (2=7)r4c4 - [nested AIC] = (8)r2c6

I'd just add a hint:
- the weak link to the nested AIC is a valid weak link to both endpoints,
- the strong link to the nested AIC complements a strong link inside, between a subset of a 3-SIS (or more).
No matter which link is on the left side or the right side.
It could be written as well: (8)r2c6 = [nested AIC] - (7=2)r4c4 - (2=8)r4c8 without flipping the nested AIC left-to-right (or with flipping it too)
In the example above:
7r4c4 is weakly linked to 7r8c4 AND to 7r4c5
8r2c6 is the candidate missing to the strong link 8r8c6=8r3c6 (SIS: 8c6)
My definition of a SIS: a set of candidates, one out of which, at least, must be true.
Cenoman
Cenoman

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Location: Paris, France

### Re: Robert's puzzles 2020-09-22

Hi Cenoman,

I'd just add a hint:
- the weak link to the nested AIC is a valid weak link to both endpoints,
- the strong link to the nested AIC complements a strong link inside, between a subset of a 3-SIS (or more).
7r4c4 is weakly linked to 7r8c4 AND to 7r4c5
8r2c6 is the candidate missing to the strong link 8r8c6=8r3c6 (SIS: 8c6)

Very good clarifications!

No matter which link is on the left side or the right side.
It could be written as well: (8)r2c6 = [nested AIC] - (7=2)r4c4 - (2=8)r4c8

Indeed. To me that orientation has always been the more natural way to read it, just like with any almost-patterns. Approaching from the weak-link side is harder. Then again, it's important to learn to see it both ways.

Cenoman wrote:BTW is 'embedded' synonym of 'nested' ?

Good question. They're very similar, and I'm sure either one gets understood.

Perhaps 'nested' implies more clearly a hierarchical containment structure of objects of the same type. For example, in programming there are nested loops and nested classes etc, which in turn may contain deeper nesting of those same types. Similarly nested AICs may contain other nested AICs, and nested T&E may contain several levels of T&E branches.

On the other hand, 'embedded' might more naturally imply a flatter hierarchy (just one containment level) and different types, like 'embedded SQL' within a programming language. I guess an analogy in sudoku might be an AIC having nodes written in another language, such as 'embedded' UFG fishes.

To add to the confusion there's also the term 'subchain' which in my vocabulary means a shorter part of a top level AIC that provides additional eliminations with different end-points (but could be written as a separate AIC too). Looks like you're using it in the same meaning. In other contexts 'subchain' could also mean a branch, so it's a bit ambiguous, but I don't think that's a problem as we can simply use 'branch' for that purpose.

I don't even remember where I originally picked the terms 'nested' and 'subchain' from, so I don't know how "official" they are. They just made sense to me so I've been using them.

SpAce

Posts: 2568
Joined: 22 May 2017

### Re: Robert's puzzles 2020-09-22

Hi Cenoman

Thanks Cenoman your explanation is clear and comprehensive.

Paolo
Ajò Dimonios

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Joined: 07 November 2019

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