The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..7|.5.|9..|
 |.5.|8.6|.4.|
 |6..|.1.|..5|
 |---+---+---|
 |.3.|...|.9.|
 |9.6|...|8.3|
 |.7.|...|.2.|
 |---+---+---|
 |7..|.8.|..4|
 |.8.|5.1|.3.|
 |..5|.4.|1..|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *---------------------------------------------------------------------*
 | 12348  124    7      | 234    5      234    |  9      168    1268   |
 | 123    5      1239   | 8     f2379   6      |ag237    4    bg127    |
 | 6      249    23489  | 23479  1      23479  | a237    8-7    5      |
 *----------------------+----------------------+-----------------------|
 | 12458  3      1248   | 12467 e267    24578  |  4567   9     b167    |
 | 9      124    6      | 1247  e27     2457   |  8      157    3      |
 | 1458   7      148    | 13469  369    34589  |  456    2     b16     |
 *----------------------+----------------------+-----------------------|
 | 7      1269   1239   | 2369   8      239    |  256    56     4      |
 |c24     8     c249    | 5    de2679   1      |  267    3     c2679   |
 | 23     269    5      | 23679  4      2379   |  1      678    26789  |
 *---------------------------------------------------------------------*


(7=23)r23c7 - (2=167)r246c9 - (6|7-249)r8c139 - (2|9)r8c5 = (267)r458c5 - 7r2c5 = 7r2c79 => -7 r3c8 ; lclste

[Cenoman]

Failed to find ste finish, so

Code: Select all

 +-------------------------+-------------------------+-----------------------+
 |  12348   124    7       |  234     5      234     |  9     c16-8 b1268    |
 |  123     5      1239    |  8       2379   6       |  237    4     127     |
 |  6       249    23489   |  23479   1      23479   |  237    78    5       |
 +-------------------------+-------------------------+-----------------------+
 |  12458   3      1248    |  12467   267    24578   |  4567   9     7-16    |
 |  9       124    6       |  1247    27     2457    |  8     d157   3       |
 |  1458    7      148     |  13469   369    34589   |  456    2    a16      |
 +-------------------------+-------------------------+-----------------------+
 |  7       1269   1239    |  2369    8      239     |  256    56    4       |
 |  24      8      249     |  5       2679   1       |  267    3     279-6   |
 |  23      269    5       |  23679   4      2379    |  1      678   2789-6  |
 +-------------------------+-------------------------+-----------------------+

Loop (1=6)r6c9 - r1c9 = (6-1)r1c8 = (1)r5c8@ => -8 r1c8, -16r4c9, -6r89c9; lclste

[SpAce]

Code: Select all

.-----------------------.--------------------.--------------------------.
|   12348  124    7     | 234    5     234   |   9        168     1268  |
| tb123    5    ta1239  | 8      2379  6     | tb23(7)    4     tb12(7) |
|   6      249   A23489 | 23479  1     23479 |   237    B(8)-7    5     |
:-----------------------+--------------------+--------------------------:
|   12458  3      1248  | 12467  267   24578 |   4567     9      167    |
|   9      124    6     | 1247   27    2457  |   8        157    3      |
|   1458   7      148   | 13469  369   34589 |   456      2      16     |
:-----------------------+--------------------+--------------------------:
|   7      1269  r1239  | 2369   8     239   |   256      56     4      |
|  s24     8     s249   | 5      2679  1     |   267      3      2679   |
|  s23     269    5     | 23679  4     2379  |   1        678    26789  |
'-----------------------'--------------------'--------------------------'

Kraken Column 3c3


(3)r2c3 - (3=127)r2c179                     a-b
||
(3-8)r3c3 = (8)r3c8                         A-B
||
(3)r7c3 - (3=249)b7p746 - (9=1237)r2c1379   r-t


=> -7 r3c8; lclste

[blue]

Code: Select all

+--------------------+---------------------------+--------------------+
| 12348  124   7     | 234      5       234      | 9     16-8  1268   |
| 123    5     1239  | 8        379-2   6        | 237   4     127    |
| 6      249   23489 | c23479   1       c23479   | 23-7  d78   5      |
+--------------------+---------------------------+--------------------+
| 12458  3     1248  | b1467-2  a267    b4578-2  | 4567  9     167    |
| 9      124   6     | b147-2   a27     b457-2   | 8     157   3      |
| 1458   7     148   | 13469    39-6    34589    | 456   2     16     |
+--------------------+---------------------------+--------------------+
| 7      1269  1239  | 2369     8       239      | 25-6  5-6   4      |
| 24     8     249   | 5        f679-2  1        | e267  3     e2679  |
| 23     269   5     | c23679   4       c2379    | 1     d678  289-67 |
+--------------------+---------------------------+---------------------+

(6=[2]7)r45c5 - 7b5p1346 = (XWing: <7>c46/r39) - (7=[8]6)r39c8 - 6r8c79 = 6r8c5 - loop

=> -2r28c4, -2b5p1346, -7r3c7, -7r9c9, -8r1c8, -6b9p129, -6r6c5; stte

Machine generated ... "stte" though !

[SpAce]

(6=[2]7)r45c5 - 7b5p1346 = (XWing: <7>c46/r39) - (7=[8]6)r39c8 - 6r8c79 = 6r8c5 - loop

=> -2r28c4, -2b5p1346, -7r3c7, -7r9c9, -8r1c8, -6b9p129, -6r6c5; stte

Wow! That's awesome! My stte is quite a bit uglier:

Code: Select all

.----------------------.---------------------.-------------------------.
|  12348  124    7     | 234     5     234   |     9      168    1268  |
|  123    5      1239  | 8      a2379  6     |  sAf237    4     r127   |
|  6      249    23489 | 23479   1     23479 |   sf237  sB78     5     |
:----------------------+---------------------+-------------------------:
|  12458  3      1248  | 12467  b267   24578 |     4567   9      167   |
|  9      124    6     | 1247   b27    2457  |     8      157    3     |
|  1458   7      148   | 13469   369   34589 |     456    2      16    |
:----------------------+---------------------+-------------------------:
|  7      1269   1239  | 2369    8     239   |    e256   e56     4     |
| E24     8     E249   | 5      c2679  1     | tFfd6-27   3    Dd2679  |
|  23     269    5     | 23679   4     2379  |     1    tC678   D26789 |
'----------------------'---------------------'-------------------------'

Kraken Row 7r2


(7)r2c5 - (7=26)r45c5 - (6)r8c5 = r8c79 - (6=52)r7c87 - (2=376)r238c7   a-f
||
(7*)r2c7 - (7=8)r3c8 - r9c8 = (89)r98c9 - (9=42)r8c13 - (2|*7=6)r8c7    A-F
||
(7)r2c9 - (7=328)b3p478 - (2|8=76)b9p48 - (6=52)r7c87 - (2=376)r238c7   r-t,e-f


=> 6r8c7; stte

[blue]

Wow! That's awesome! My stte is quite a bit uglier:
(...)
=> 6r8c7; stte

Neat -- especially that +6r8c7 gives the stte finish !

I had another candidate that covered some of the same ground ... 7r2, r3c8, and the 8's & 9's in b9
That, along with a couple of almost hidden pairs (including in c5):

Code: Select all

+--------------------+----------------------+----------------------+
| 12348  124   7     | 234    5       234   | 9      16-8  1268    |
| 123    5     1239  | 8      f379-2  6     | g237   4     g127    |
| 6      249   23489 | 23479  1       23479 | 23-7   a78   5       |
+--------------------+----------------------+----------------------+
| 12458  3     1248  | 12467  267     24578 | 4567   9     167     |
| 9      124   6     | 1247   27      2457  | 8      157   3       |
| 1458   7     148   | 13469  f39-6   34589 | 456    2     16      |
+--------------------+----------------------+----------------------+
| 7      1269  1239  | 2369   8       239   | 256    56     4      |
| 24     8     249   | 5      e679-2  1     | e67-2  3     d679-2  |
| 23     269   5     | 23679  4       2379  | 1      b678  c89-267 |
+--------------------+----------------------+----------------------+

7r2c5 = 7r2c79 - (7=8)r3c8 - r9c8 = (8-9)r9c9 = (9-67)r8c9 = 67r8c57 - 9r8c5 = 39r26c5 - loop

=> -7r3c7, -8r1c8, -267r9c9, -2r8c579, -6r6c5, -2r2c5; stte

The "stte" is from the -2's in b9, and -7r3c7.

[eleven]

Coming late ...

Code: Select all

 *---------------------------------------------------------------------------*
 |  12348   124    7       |  234     5      234     |  9     e168 fd1268    |
 |  123     5      1239    |  8     ja39-27  6       |  237    4   fd12-7    |
 |  6       249    23489   |  23479   1      23479   |  237    78    5       |
 |-------------------------+-------------------------+-----------------------|
 |  12458   3      1248    |  12467   267    24578   |  4567   9   gC167     |
 |  9       124    6       |  1247    27     2457    |  8      157   3       |
 |  1458    7      148     |  13469 ja39-6   34589   |  456    2   gC16      |
 |-------------------------+-------------------------+-----------------------|
 |  7       1269   1239    |  2369    8      239     |  256    56    4       |
 |hB24      8    hB249     |  5     iB2679   1       |  67-2   3   hC2679    |
 |  23      269    5       |  23679   4      2379    |  1      678   26789   |
 *---------------------------------------------------------------------------*

hp39r26c5 = 249r8c135 - (2|9=6)r468c9 - r12c9 = (6-1)r1c8 = r12c9 - (1=67)r46c9 - (6|7=249)r8c139 - 9r8c5 = hp39r26c5
=> -27r2c5, -6r6c5, -2r8c7, -7r2c9; stte

[SpAce]

hp39r26c5 = 249r8c135 - (2|9=6)r468c9 - r12c9 = (6-1)r1c8 = r12c9 - (1=67)r46c9 - (6|7=249)r8c139 - 9r8c5 = hp39r26c5
=> -27r2c5, -6r6c5, -2r8c7, -7r2c9; stte

Hi eleven! This is probably a dumb question, but could you explain to me how you get the last two eliminations with that chain?

[blue]

deleted

[eleven]

All but a dumb question, cause it is not written in the chain.

For -2r8c7 the triple 249r8c135 instead of 9r8c5 at the end is not written (if the 9 is not in the triple r8c139, it must be in r8c5, forcing a triple 249r8c135). In both cases 2 cannot be in r8c7.
[edit: no, that's not true with the 9 in r8c3] Probably i would have to write an additional node 249r8c135 - (2|9=67)r8c89 - (2|9=6)r468c9 for this (unnecessary) elimination.
For -7r2c9: on the right side there is 67r46c9, on left side we 6r12c9 and 1r46c9, forcing 7 to r4c9. So better would probably be to write (17=67)r46c9, which looks strange too.
At some point i did not bother anymore, how to formulate the AIC.

The idea was simple:
With 16 restricted to r1c89,r2c9 in box 3 it was clear, that each pair 16 in rows 4-9 pf column 9 would lead to a contradiction in r1c8. This directly leads to the eliminations, Cenoman showed with his loop. Cause they don't make it stte, i looked, what else would lead to a 16 placement there, and found the almost hidden pair 39.

[SpAce]

The idea was simple:
With 16 restricted to r1c89,r2c9 in box 3 it was clear, that each pair 16 in rows 4-9 pf column 9 would lead to a contradiction in r1c8. This directly leads to the eliminations, Cenoman showed with his loop. Cause they don't make it stte, i looked, what else would lead to a 16 placement there, and found the almost hidden pair 39.

Thanks for the explanations! I can easily see it as two steps -- the loop (or contradiction) forcing 7r4c9 (eliminating 7r2c9) and the hp-chain eliminating 7r2c5 -- which together give us stte, but I still can't see how they could be combined into a single chain doing both at once. I only know two ways how chains can eliminate something not directly linked to the end-points: a rank-0 loop or a multi-headed "hydra" containing sub-chains with different end-points. This doesn't look like either of those kinds to me.

[eleven]

This is my single chain:
-(1&6)r1c8 => (16r126c9 & 7r4c9) => -67r8c9 => 67r8c56 => 39r26c5
All must be true.

I'l never try again to translate that into the unloved AIC notation.

[SpAce]

This is my single chain:
-(1&6)r1c8 => (16r126c9 & 7r4c9) => -67r8c9 => 67r8c56 => 39r26c5
All must be true.

That makes perfect sense.

I'l never try again to translate that into the unloved AIC notation.

As far as I'm concerned, the AIC notation is not generally unloved, but in this case I must agree that your notation above probably beats any attempt to express the same logic as an AIC. Here's mine (as a multi-headed "hydra"):

Code: Select all

.----------------------.--------------------------.---------------------------.
|  12348  124    7     | 234       5       234    |  9     fd168      c1268   |
|  123    5      1239  | 8      ka(39)-27  6      |  237     4         12-7   |
|  6      249    23489 | 23479     1       23479  |  237     78        5      |
:----------------------+--------------------------+---------------------------:
|  12458  3      1248  | 1246-7    26-7    2458-7 |  456-7   9     hba(7)-16  |
|  9      124    6     | 1247      27      2457   |  8      g15-7      3      |
|  1458   7      148   | 13469  ka(39)-6   34589  |  456     2       hb16     |
:----------------------+--------------------------+---------------------------:
|  7      1269   1239  | 2369      8       239    |  256    e56        4      |
| i24     8     i249   | 5      jcb267-9   1      | d267     3       id269-7  |
|  23     269    5     | 23679     4       2379   |  1      e678       2689-7 |
'----------------------'--------------------------'---------------------------'

(39)r26c5&(@7)r4c9 = (9)r8c5|(16)r46c9 - (6)r8c5&r1c9 = r8c79|r1c8 - r79c8 = (6-1)r1c8 = r5c8 - (1=6@7)r64c9 - (6|7=429)r8c139 - r8c5 = (39)r26c5

-> 39r26c5 & 7r4c9 => -27 r2c5, -6 r6c5, -9 r8c5; -16 r4c9, -7 r4c4567,r289c9,r5c8; stte

(The critical eliminations being -7 r2c59)

Ugly as hell, but do you think it's correct?