The New Sudoku Players' Forum

[P.O.]

Code: Select all

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

....924.8....1.53.8..3.67..4.3..5.8..2....3..6..9.3..5.4.....5...1.7.8..9..2....4

1357    13567   567     57      9       2       4       16      8               
27      679     24679   478     1       478     5       3       269             
8       159     2459    3       45      6       7       129     129             
4       179     3       167     26      5       1269    8       12679           
157     2       5789    14678   468     1478    3       14679   1679             
6       178     78      9       248     3       12      1247    5               
237     4       2678    168     368     189     1269    5       123679           
235     356     1       456     7       49      8       269     2369             
9       35678   5678    2       3568    18      16      167     4     


[SteveG48]

Code: Select all

 
 *-----------------------------------------------------------------------------*
 | 1357    13567 hk567     |e57      9       2       | 4       16      8       |
 | 27     g679     24679   |f478     1      f478     | 5       3       269     |
 | 8       159     2459    | 3      e45      6       | 7       129     129     |
 *-------------------------+-------------------------+-------------------------|
 | 4      b17-9    3       | 167     26      5       |a1269    8      a12679   |
 | 157     2     hk5789    | 14678   468     1478    | 3       14679   1679    |
 | 6      i178   hk78      | 9       248     3       | 12      1247    5       |
 *-------------------------+-------------------------+-------------------------|
 | 237     4       2678    | 168     368    c189     |b1269    5       123679  |
 | 235     356     1       |d456     7      d49      | 8       269     2369    |
 | 9      j35678  k5678    | 2       3568   j18      |j16      167     4       |
 *-----------------------------------------------------------------------------*


9r4c7 = 9*r4c2&9r7c7 - 9r7c6 = (94-5)r8c46 = (54)b2p18 - (4=78)r2c46 - (7|*9=6**)r2c2 = (6*9=578)r156c3 - 8r6c2 (186)r9c267 - (6|**6=5789)r1679c3 => -9 r4c2 ; ste

[yzfwsf]

Whip[9]: Supposing 5r1c4 will result in 6 to disappear in Box 7 => r1c4<>5
5$r1c4 - 5c5(r3=r9%) - 3r9(c5=c2#) - 8c2(r9=r6) - r6c3(8=7) - r1c3(5$7=6@) - r1c8(6=1) - 1r3(c89=c2) - 5c2(r1$9%3=r8) - 6b7(p3@8#9@5=.)
stte

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 1357   13567  567    ! 57     9      2      ! 4      16     8      !
   ! 27     679    24679  ! 478    1      478    ! 5      3      269    !
   ! 8      159    2459   ! 3      45     6      ! 7      129    129    !
   +----------------------+----------------------+----------------------+
   ! 4      179    3      ! 167    26     5      ! 1269   8      12679  !
   ! 157    2      5789   ! 14678  468    1478   ! 3      14679  1679   !
   ! 6      178    78     ! 9      248    3      ! 12     1247   5      !
   +----------------------+----------------------+----------------------+
   ! 237    4      2678   ! 168    368    189    ! 1269   5      123679 !
   ! 235    356    1      ! 456    7      49     ! 8      269    2369   !
   ! 9      35678  5678   ! 2      3568   18     ! 16     167    4      !
   +----------------------+----------------------+----------------------+
173 candidates.

Simplest-first solution, in Z4:

Code: Select all

biv-chain[3]: r3c5{n4 n5} - b8n5{r9c5 r8c4} - b8n4{r8c4 r8c6} ==> r2c6≠4
biv-chain[4]: r1c4{n7 n5} - b8n5{r8c4 r9c5} - r9n3{c5 c2} - b1n3{r1c2 r1c1} ==> r1c1≠7
finned-swordfish-in-columns: n7{c1 c6 c9}{r7 r2 r5} ==> r5c8≠7
biv-chain[3]: c8n7{r9 r6} - r6c3{n7 n8} - c2n8{r6 r9} ==> r9c2≠7
finned-x-wing-in-rows: n7{r9 r6}{c8 c3} ==> r5c3≠7
biv-chain[4]: r9n7{c8 c3} - r6c3{n7 n8} - c2n8{r6 r9} - r9c6{n8 n1} ==> r9c8≠1
z-chain[4]: r6n7{c3 c8} - r9c8{n7 n6} - r1c8{n6 n1} - c1n1{r1 .} ==> r5c1≠7
z-chain[4]: r1n3{c2 c1} - c1n1{r1 r5} - c1n5{r5 r8} - c4n5{r8 .} ==> r1c2≠5
finned-x-wing-in-columns: n5{c5 c2}{r3 r9} ==> r9c3≠5
hidden-pairs-in-a-row: r9{n3 n5}{c2 c5} ==> r9c5≠8, r9c5≠6, r9c2≠8, r9c2≠6
singles ==> r6c2=8, r6c3=7, r9c8=7,> r7c1=7, r2c1=2, r7c3=2, r9c3=8, r9c6=1, r9c7=6, r8c2=6
whip[1]: c7n2{r6 .} ==> r4c9≠2, r6c8≠2
whip[1]: r6n1{c8 .} ==> r4c7≠1, r4c9≠1, r5c8≠1, r5c9≠1
x-wing-in-columns: n5{c2 c5}{r3 r9} ==> r3c3≠5
naked-triplets-in-a-column: c9{r2 r4 r5}{n6 n9 n7} ==> r8c9≠9, r7c9≠9, r3c9≠9
biv-chain[3]: r2n6{c3 c9} - b3n9{r2c9 r3c8} - r3c3{n9 n4} ==> r2c3≠4
stte

1-step solutions require using W9, i.e. absurdly long chains, considering the existence of a solution in Z4:

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whip[9]: c5n5{r3 r9} - r9n3{c5 c2} - c2n8{r9 r6} - r6c3{n8 n7} - r1c3{n7 n6} - r1c8{n6 n1} - r3n1{c9 c2} - c2n5{r3 r8} - c2n6{r8 .} ==> r1c4≠5
stte

Code: Select all

whip[9]: c1n3{r8 r1} - c1n1{r1 r5} - c1n5{r5 r8} - c4n5{r8 r1} - c2n5{r1 r3} - c2n1{r3 r1} - r1n7{c2 c3} - r6c3{n7 n8} - b7n8{r7c3 .} ==> r9c2≠3
stte

[P.O.]

1-step solutions require using W9, i.e. absurdly long chains, considering the existence of a solution in Z4:

add the lengths of the techniques of your simplest-first solution and count the number of eliminations necessary to obtain the solution, this is absurdly complicated for a puzzle solved with only one elimination found by a technique of length 9.

[denis_berthier]

1-step solutions require using W9, i.e. absurdly long chains, considering the existence of a solution in Z4:

add the lengths of the techniques of your simplest-first solution and count the number of eliminations necessary to obtain the solution, this is absurdly complicated for a puzzle solved with only one elimination found by a technique of length 9.

Adding the lengths is meaningless, as complexity increases exponentially with length.

[P.O.]

1-step solutions require using W9, i.e. absurdly long chains, considering the existence of a solution in Z4:

add the lengths of the techniques of your simplest-first solution and count the number of eliminations necessary to obtain the solution, this is absurdly complicated for a puzzle solved with only one elimination found by a technique of length 9.

Adding the lengths is meaningless, as complexity increases exponentially with length.

building a chain is a linear process, it grows one link at a time, and so does its complexity.

[denis_berthier]

.
At each step in a chain, there are several possibilities of extension => exponential growth

[P.O.]

the complexity of the chain is a property of itself, not of the number of links available to make it grow.

[denis_berthier]

.
what counts is the complexity of FINDING the chain, of course

[P.O.]

like i said you add a link one after the other and you find the chain, that the complexity of finding it.

[SteveG48]

.
what counts is the complexity of FINDING the chain, of course

What also counts is whether you can find a single path or are forced into addressing multiple extensions. Today's puzzle made me use two starred values to bring paths back together. Not pleasing. Hopefully someone else will do better.

[Cenoman]

My two cents:

Code: Select all

 +-------------------------+------------------------+--------------------------+
 | a1357  a13567 Ab567     | u57      9      2      |  4      16      8        |
 |  27     679     24679   |  478     1      478    |  5      3       269      |
 |  8     a159    b2459    |  3       45     6      |  7      129     129      |
 +-------------------------+------------------------+--------------------------+
 |  4     y179     3       |  167     26     5      | x1269   8       12679    |
 |  157    2      z789-5   |  14678   468    1478   |  3      14679   1679     |
 |  6     C178    B78      |  9       248    3      |  12     1247    5        |
 +-------------------------+------------------------+--------------------------+
 |  237    4       2678    |  168     368    189    | w1269   5       123679   |
 | v235   v356     1       | u456     7      49     |  8     v269    v2369     |
 |  9     D35678  E5678    |  2       3568  E18     | E16    E167     4        |
 +-------------------------+------------------------+--------------------------+

Kraken row (7)r1c1234
(7-135)b1p128 = (5)r13c3
(7)r1c3 - (7=8)r6c3 - r6c2 = r9c2 - (8=1675)r9c3678
(75)r18c4 - (5=2369)r8c1289 - r7c7 = r4c7 - r4c2 = (9)r5c3
=> -5 r5c3; ste

Added:

Hidden Text: Show

Krakenless, two steps:
1. (31)r1c12 = r1c8 - r1c1 = (1-5)r5c1 = r5c3 - r13c3 = (513)b1p128 => -7 r1c12
2. (7=8)r6c3 - r6c2 = (8-3)r9c2 = (3-5)r9c5 = r3c5 - (5=7)r1c4 => -7 r1c3; ste

[SteveG48]

At least 2 dollars' worth, I'd say.

[P.O.]

thank you for your answers, my solution:

Code: Select all

3r9c2 => r2c2 <> 6,7,9
 r9c2=3 - r1n3{c2 c1} - c1n1{r1 r5} - c1n5{r5 r8} - r8c2{n35 n6}
 r9c2=3 - r1n3{c2 c1} - c1n1{r1 r5} - c1n5{r5 r8} - c4n5{r8 r1} - b2n7{r1c4 r2c46}
 r9c2=3 - r1n3{c2 c1} - c1n1{r1 r5} - r5n5{c1 c3} - b4n9{r5c3 r4c2}

=> r9c2 <> 3
ste.