The New Sudoku Players' Forum

[P.O.]

from the Patterns Game, SER 8.4

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. 2 .   4 . .   7 8 .
6 . .   . 3 .   . . 1
. . .   . . .   . . .
9 . .   . 2 .   . . 4
. 8 .   6 . .   2 5 .
. . .   . . .   . . .
3 . .   . 1 .   . . 2
4 . .   . 9 .   . 6 .
. 7 .   5 . .   3 . .

.2.4..78.6...3...1.........9...2...4.8.6..25..........3...1...24...9..6..7.5..3..

15       2        1359     4        56       1569     7        8        3569             
6        459      45789    2789     3        25789    459      249      1                 
1578     13459    1345789  12789    5678     1256789  4569     2349     3569             
9        1356     13567    1378     2        13578    168      137      4                 
17       8        1347     6        47       13479    2        5        379               
1257     13456    1234567  13789    4578     1345789  1689     1379     36789             
3        569      5689     78       1        4678     4589     479      2                 
4        15       1258     2378     9        2378     158      6        578               
128      7        12689    5        468      2468     3        149      89     


[Cenoman]

My first solution (to be forgotten)

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 +---------------------------+---------------------------+------------------------+
 |  15     2       139-5     |  4       56     1569      |  7      8      39-56   |
 |  6      459     45789     |  2789    3      25789     |  459    249    1       |
 |  1578   13459   1345789   |  12789   5678   1256789   |  4569   2349   3569    |
 +---------------------------+---------------------------+------------------------+
 |  9      1356    13567     |  1378    2      13578     |  168    137    4       |
 |  17     8       1347      |  6       47     13479     |  2      5      39-7    |
 |  1257   13456   1234567   |  13789   4578   1345789   |  1689   1379   36789   |
 +---------------------------+---------------------------+------------------------+
 |  3      569     5689      |  78      1      4678      |  4589   479    2       |
 |  4      15      1258      |  2378    9      2378      |  158    6      578     |
 |  128    7       12689     |  5       468    2468      |  3      149    89      |
 +---------------------------+---------------------------+------------------------+

1. Kraken cell (468)r9c5
(4)r9c5 - (4=7)r5c5 - (7=1)r5c1 - (1=5)r1c1
(6)r9c5 - (6=5)r1c5
(8)r9c5 - (8=9)r9c9 - r5c9 = r5c6 - (9=165)r1c156
=>-5r1c39

2. Kraken cell (468)r9c5
(4)r9c5 - (4=7)r5c5
(6)r9c5 - (6=5)r1c5 - (5=1)r1c1 - (1=7)r5c1
(8)r9c5 - (8=7)r7c4 - r7c8 = (7)r8c9
=> -7 r5c9

3. Multikraken row (1)r9c138 & row (1)r5c136 & cell (36789)r6c9, presented as a net:

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X-Wing (1)r59\c13 - (1=5)r1c1 - (5=6)r1c5 *
 ||
(1)r5c6 - (1=473)r5c135 - r1c3 = (3)r1c9 *
 ||
(1)r9c8 - (1=793)b6p268 - (3)r6c9
                           ||
                          (6)r6c9 *
                           ||
                          (7)r6c9 - (7=158)r8c279 - (8=9)r9c9 - r5c9 = r5c6 - (9=156)r1c156 *
                           ||                                 /
                          (89)r69c9 - - - - - - - - - - - - -

=> -6 r1c9; lclste

For French speakers, obviously, "j'étais à coté de mes pompes" (word-for-word: 'I was beside my shoes') i.e. I was way out to lunch when I posted my first solution (much too complex). I should have found the same two steps as proposed in following posts:

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 +---------------------------+---------------------------+------------------------+
 |YC15     2       139-5     |  4     YB56    Y1569      |  7      8     Z3569    |
 |  6      459     45789     |  2789    3      25789     |  459    249    1       |
 |  1578   13459   1345789   |  12789   5678   1256789   |  4569   2349   3569    |
 +---------------------------+---------------------------+------------------------+
 |  9      1356    13567     |  1378    2      13578     |  168    137    4       |
 | D17     8       1347      |  6      b47    X13479     |  2      5    ZW39-7    |
 |  1257   13456   1234567   |  13789   4578   1345789   |  1689   1379   36789   |
 +---------------------------+---------------------------+------------------------+
 |  3      569     5689      | x78      1      4678      |  4589  y479    2       |
 |  4      15      1258      |  2378    9      2378      |  158    6     z578     |
 |  128    7       12689     |  5    wAa468    2468      |  3      149    8-9     |
 +---------------------------+---------------------------+------------------------+

1. Kraken (468)r9c5
(4)r9c5 - (4=7)r5c5
(6)r9c5 - (6=5)r1c5 - (5=1)r1c1 - (1=7)r5c1
(8)r9c5 - (8=7)r7c4 - r7c8 = (7)r8c9
=> -7 r5c9
------------------
2. (9)r5c9 = r5c6 - (9=156)r1c156 - (5|6=39)r15c9 => -9 r9c9

[DEFISE]

Hi Cenoman,
I think I have a little simpler path, look at this:
1)
7r5c9* - 7r5c1 = 1r5c1 – 1r1c1 = 5r1c1 – 5r1c5 = 57r36c5 – 8r36c5 = 8r9c5 – 8r7c4 = 7r7c4*
The two candidates with a * see all 7 in r8.
So if 7r5c9 were true then all 7 in r8 would be false.
=> -7r5c9
2)
9r9c9* - 9r5c9 = 3r5c9 – 3r1c9 = 3r1c3 – 9r1c3
then an OR branching with two cases:
= 9r1c6* (the two candidates with a * see all 9 in r5, so if 9r9c9 were true then all 9 in r5 would be false).
= 9r1c9 (obviously impossible if 9r9c9 were true).
=> -9r9c9

Singles, box/lines, naked pairs to the end.

[yzfwsf]

1)Cell Forcing Chain: Each candidate in r9c5 true in turn will all lead to: r5c9<>7
4r9c5 - (4=7)r5c5
6r9c5 - (6=5)r1c5 - (5=1)r1c1 - (1=7)r5c1
8r9c5 - (8=7)r7c4 - 7r7c8 = 7r8c9
2)Cell Forcing Chain: Each candidate in r1c9 true in turn will all lead to: r369c9<>9
3r1c9 - (3=9)r5c9
5r1c9 - (5=169)r1c156 - 9r5c6 = 9r5c9
6r1c9 - (6=159)r1c156 - 9r5c6 = 9r5c9
9r1c9
LC + NP to the end

[denis_berthier]

.

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Resolution state after Singles and whips[1]:
   +-------------------------+-------------------------+-------------------------+
   ! 15      2       1359    ! 4       56      1569    ! 7       8       3569    !
   ! 6       459     45789   ! 2789    3       25789   ! 459     249     1       !
   ! 1578    13459   1345789 ! 12789   5678    1256789 ! 4569    2349    3569    !
   +-------------------------+-------------------------+-------------------------+
   ! 9       1356    13567   ! 1378    2       13578   ! 168     137     4       !
   ! 17      8       1347    ! 6       47      13479   ! 2       5       379     !
   ! 1257    13456   1234567 ! 13789   4578    1345789 ! 1689    1379    36789   !
   +-------------------------+-------------------------+-------------------------+
   ! 3       569     5689    ! 78      1       4678    ! 4589    479     2       !
   ! 4       15      1258    ! 2378    9       2378    ! 158     6       578     !
   ! 128     7       12689   ! 5       468     2468    ! 3       149     89      !
   +-------------------------+-------------------------+-------------------------+
 228 candidates

1) 2-step solution:
whip[9]: r8c2{n5 n1} - r9n1{c3 c8} - r8c7{n1 n8} - r8c3{n8 n2} - r9n2{c3 c6} - r9n4{c6 c5} - r5c5{n4 n7} - c9n7{r5 r6} - c9n8{r6 .} ==> r8c9≠5
whip[1]: c9n5{r3 .} ==> r2c7≠5, r3c7≠5
whip[12]: r5n9{c9 c6} - r1n9{c6 c3} - r1n3{c3 c9} - r5c9{n3 n7} - r5c1{n7 n1} - r1c1{n1 n5} - r2n5{c3 c6} - b5n5{r4c6 r6c5} - c5n7{r6 r3} - c5n8{r3 r9} - r7c4{n8 n7} - c8n7{r7 .} ==> r9c9≠9
w1-tte


2) 1-step solution:
FORCING[3]-T&E(S) applied to trivalue candidates n3r5c9, n7r5c9 and n9r5c9 :
===> 13 values decided in the three cases: n8r3c1 n7r3c5 n4r5c5 n2r9c1 n4r9c6 n8r8c3 n4r6c2 n2r6c3 n1r8c2 n1r9c8 n3r8c4 n2r8c6 n8r2c6
===> 123 candidates eliminated in the three cases: n1r1c3 n5r1c3 n9r1c3 n5r1c6 n9r1c6 n5r1c9 n6r1c9 n4r2c2 n5r2c3 n8r2c3 n9r2c3 n7r2c4 n8r2c4 n2r2c6 n5r2c6 n7r2c6 n9r2c6 n4r2c8 n9r2c8 n1r3c1 n5r3c1 n7r3c1 n1r3c2 n4r3c2 n5r3c2 n5r3c3 n7r3c3 n8r3c3 n9r3c3 n1r3c4 n7r3c4 n8r3c4 n5r3c5 n6r3c5 n8r3c5 n2r3c6 n6r3c6 n7r3c6 n8r3c6 n9r3c6 n5r3c7 n9r3c7 n9r3c8 n3r3c9 n9r3c9 n1r4c2 n5r4c2 n1r4c3 n3r4c3 n7r4c3 n3r4c4 n7r4c4 n1r4c6 n3r4c6 n8r4c6 n6r4c7 n1r4c8 n4r5c3 n7r5c3 n7r5c5 n1r5c6 n4r5c6 n7r5c6 n1r6c1 n2r6c1 n1r6c2 n3r6c2 n5r6c2 n6r6c2 n1r6c3 n3r6c3 n4r6c3 n5r6c3 n6r6c3 n7r6c3 n3r6c4 n8r6c4 n9r6c4 n4r6c5 n7r6c5 n1r6c6 n4r6c6 n5r6c6 n7r6c6 n8r6c6 n8r6c7 n9r6c7 n1r6c8 n7r6c8 n3r6c9 n7r6c9 n9r6c9 n9r7c2 n6r7c3 n8r7c3 n4r7c6 n8r7c6 n5r7c7 n7r7c8 n5r8c2 n1r8c3 n2r8c3 n5r8c3 n2r8c4 n7r8c4 n8r8c4 n3r8c6 n7r8c6 n8r8c6 n1r8c7 n8r8c7 n8r8c9 n1r9c1 n8r9c1 n1r9c3 n2r9c3 n8r9c3 n4r9c5 n2r9c6 n6r9c6 n8r9c6 n4r9c8 n9r9c8
stte

[yzfwsf]

(8=9)r9c9 - n9r5(c9=c6) - n9r1(c6=c3) - n3r1(c3=c9) - r5c9(3=7) - r5c15(7=4*1) - r1c1(1=5) -r1c5(5=6) - r9c5(6=8) - 8r9c9,loop=> r1c369<>5, r369c1<>1,r3c5<>6,r36c9<>9,r5c36<>7,r5c6<>4,r9c136<>8
LC+HP=>stte

[P.O.]

thank you for your answers, it is informative to see different techniques and in particular the one step loop of yzfwsf is very impressive to me; i also think that the resolutions given by the forcing chains are the simplest, easy to read, easy to understand if not always easy to find.
my solution:

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468r9c5 => r5c9 <> 7
 r9c5=4 - r5c5{n4 n7} -
 r9c5=6 - r1c5{n6 n5} - r1c1{n5 n1} - r5c1{n1 n7}
 r9c5=8 - r7c4{n8 n7} - b9n7{r7c8 r8c9}

9r1c369 => r369c9 <> 9
 r1c3=9 - r1n3{c3 c9} - r5c9{n3 n9}
 r1c6=9 - r5n9{c6 c9}
 r1c9=9


bte.

Hidden Text: Show

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( n8r9c9  n8r3c1  n8r6c5  n8r4c7 )
intersections:
((((7 0) (2 3 1) (4 5 7 9)) ((7 0) (3 3 1) (1 3 4 5 7 9)))
 (((6 0) (6 7 6) (1 6 9)) ((6 0) (6 9 6) (3 6 7 9)))
 (((5 0) (4 6 5) (1 3 5 7)) ((5 0) (6 6 5) (1 3 4 5 7 9))))
PAIR ROW: ((8 2 7) (1 5)) ((8 7 9) (1 5)) 
(((8 3 7) (1 2 5 8)) ((8 9 9) (5 7)))
( n7r8c9 )
intersections:
((((5 0) (7 7 9) (4 5 9)) ((5 0) (8 7 9) (1 5)))
 (((5 0) (2 2 1) (4 5 9)) ((5 0) (2 3 1) (4 5 7 9)))
 ( n8r7c4   n3r6c6   n7r6c4   n9r2c4   n2r8c6   n3r8c4   n7r7c6
   n1r3c6   n2r3c4   n8r2c6   n1r6c7   n9r5c6   n1r4c4   n6r1c6
   n4r7c8   n9r7c7   n6r6c9   n9r6c8   n3r5c9   n7r4c8   n3r4c2
   n3r3c8   n2r2c8   n4r2c7   n9r1c9   n1r9c8   n5r8c7   n1r8c2
   n1r5c3   n6r3c7   n3r1c3   n9r3c2   n9r9c3   n6r4c3   n6r7c2
   n5r2c2   n5r7c3   n4r3c3   n7r2c3   n5r3c9   n5r4c6   n4r6c2
   n2r6c3   n8r8c3   n5r6c1   n7r3c5   n5r1c5   n4r9c6   n6r9c5
   n2r9c1   n4r5c5   n7r5c1   n1r1c1 ))

1 2 3   4 5 6   7 8 9
6 5 7   9 3 8   4 2 1
8 9 4   2 7 1   6 3 5
9 3 6   1 2 5   8 7 4
7 8 1   6 4 9   2 5 3
5 4 2   7 8 3   1 9 6
3 6 5   8 1 7   9 4 2
4 1 8   3 9 2   5 6 7
2 7 9   5 6 4   3 1 8


[totuan]

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 *--------------------------------------------------------------------------------------*
 | 15       2       #1359     | 4        56      *1569     | 7        8       *3569     |
 | 6        459      45789    | 2789     3        25789    | 459      249      1        |
 | 1578     13459    1345789  | 12789    5678     1256789  | 4569     2349     356-9    |
 |----------------------------+----------------------------+----------------------------|
 | 9        1356     13567    | 1378     2        13578    | 168      137      4        |
 | 17       8        1347     | 6        47      *13479    | 2        5       *39       |
 | 1257     13456    1234567  | 13789    4578     1345789  | 1689     1379     3678-9   |
 |----------------------------+----------------------------+----------------------------|
 | 3        569      5689     | 78       1        4678     | 4589     479      2        |
 | 4        15       1258     | 2378     9        2378     | 158      6        578      |
 | 128      7        12689    | 5        468      2468     | 3        149      8-9      |
 *--------------------------------------------------------------------------------------*

2. (9)r5c9 = r5c6 - (9=156)r1c156 - (5|6=39)r15c9 => -9 r9c9

2)
9r9c9* - 9r5c9 = 3r5c9 – 3r1c9 = 3r1c3 – 9r1c3
then an OR branching with two cases:
= 9r1c6* (the two candidates with a * see all 9 in r5, so if 9r9c9 were true then all 9 in r5 would be false).
= 9r1c9 (obviously impossible if 9r9c9 were true).
=> -9r9c9

2)Cell Forcing Chain: Each candidate in r1c9 true in turn will all lead to: r369c9<>9
3r1c9 - (3=9)r5c9
5r1c9 - (5=169)r1c156 - 9r5c6 = 9r5c9
6r1c9 - (6=159)r1c156 - 9r5c6 = 9r5c9
9r1c9

Code: Select all

9r1c369 => r369c9 <> 9
 r1c3=9 - r1n3{c3 c9} - r5c9{n3 n9}
 r1c6=9 - r5n9{c6 c9}
 r1c9=9


Another way to present above as reference – an almost X-wing:

(X-wing 9’s: r15c69)=(9-3)r1c3=r1c9-(3=9)r5c9 => r369c9<>9

Thanks for the puzzle!
totuan

[Cenoman]

Back to the blackboard.

...the one step loop of yzfwsf is very impressive to me.

Same to me !

(8=9)r9c9 - n9r5(c9=c6) - n9r1(c6=c3) - n3r1(c3=c9) - r5c9(3=7) - r5c15(7=4*1) - r1c1(1=5) -r1c5(5=6) - r9c5(6=8) - 8r9c9,loop=> r1c369<>5, r369c1<>1,r3c5<>6,r36c9<>9,r5c36<>7,r5c6<>4,r9c136<>8
LC+HP=>stte

In order to catch yzfwsf's solution, I have written it my way:
It's a memory chain, that I'd write comprehensively as a net:

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      - - - - - - - - - - - - (9)r1c9
     /                         ||
(8=9)r9c9 - r5c9 = r5c6 - r1c6 = (9-3)r1c3 = r1c9 - (3=7)r5c9 - (7=41)r5c15 - (1=5)r1c1 - (5=6)r1c5 - (6=8)r9c5 
     \                                                ||            \                                   ||
      - - - - - - - - - - - - - - - - - - - - - - - -(9)r5c9         - - - - - - - - - - - - - - - - - -(4)r9c5

Without memories, it could be written as a kraken (cell r9c5):

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(4)r9c5 - - - - - - - - - - (4=7)r5c5
 ||                               \
(6)r9c5 - (6=5)r1c5 - (5=17)r15c1 - (7)r5c9 = [(9*=*3)r5c9 - r1c9 = (3-9)r1c3 = XW(9)r15\c69] - (9=8)r9c9
 ||
(8)r9c5
-------------
=> (8)r9c5 == (8)r9c9

Here is the Triangular Matrix of this move (TM 10x10) with yzfwsy's 15 eliminations shown in the bottom line:

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  8r9c9   9r9c9
          9r5c9   9r5c6
          9r1c9   9r1c6    9r1c3
                           3r1c3   3r1c9
          9r5c9                    3r5c9   7r5c9
                                           7r5c5   4r5c5
                                           7r5c1          1r5c1
                                                          1r1c1    5r1c1
                                                                   5r1c5    6r1c5
  8r9c5                                            4r9c5                    6r9c5
---------------------------------------------------------------------------------
-8r9c136 -9r36c9                          -7r5c36 -4r6c5 -1r369c1 -5r1c369 -6r3c5

This matrix is not far from a symmetric pigeonhole matrix. The double presence of 9r5c9 in the second column prevents it. Nevertheless, column 2 and columns 6 to 10 can be brought as the first column, hence the eliminations at their bottom. It not possible for columns 3,4,5 without placing 9r5c9 as a top entry of a column, which would make an invalid TM.

So, I agree with yzfwsf's list of eliminations. My question to you is: how did you build your list of eliminations, which is not so obvious to derive from your "chain" writing (and maybe not much more from the nets writing) ?
Anyhow, kudos for your finding

[yzfwsf]

Hi Cenoman
For details, please refer to the following post:
https://tieba.baidu.com/p/7482719816