The New Sudoku Players' Forum

[shye]

Code: Select all

+-------+-------+-------+
| . . . | 7 . 5 | . 2 . |
| . 1 . | . 6 . | . . 5 |
| . . 9 | . . . | 3 . . |
+-------+-------+-------+
| 2 . . | 3 . 4 | . . 7 |
| . 7 . | . 8 . | . . . |
| 3 . . | 6 . . | . . 8 |
+-------+-------+-------+
| . . 4 | . . . | 9 . . |
| 8 . . | . . . | . 1 . |
| . 3 . | 5 . 2 | . . . |
+-------+-------+-------+
...7.5.2..1..6...5..9...3..2..3.4..7.7..8....3..6....8..4...9..8......1..3.5.2...

estimated rating: 8.8
something more reminiscent of my older puzzles!

[yzfwsf]

Whip[7]: Supposing 1r1c5 would causes 1 to disappear in Box 4 => r1c5<>1
1r1c5 - r3c6(1=8) - 8r7(c6=c4) - 1c4(r7=r5) - r5c6(1=9) - 9c1(r5=r9) - 1r9(c1=c3) - 1b4(p9=.);btte

[eleven]

Even reading these chains is hard, unless you click on the digits in a solver, because you don't even know, which one you should remember and erase it in your mind in the 3 units. Have you tried that without solver ? My simple solver did not allow me to set 1r9c3, because it would leave no 1 in c1.

Code: Select all

 *-------------------------------------------------------------------------------*
 |  46      468     368    |  7     d1349    5       |  1468    2      c1469     |
 |  47      1       2378   |  2489   6       389     |  478     4789    5        |
 |  4567    24568   9      |  1248   124     18      |  3       4678   c146      |
 |-------------------------+-------------------------+---------------------------|
 |  2       5689    1568   |  3      159     4       |  156     569     7        |
 | b14569   7       156    | a129    8      a19      |  12456   34569  b123469   |
 |  3       459     15     |  6      12579   179     |  1245    459     8        |
 |-------------------------+-------------------------+---------------------------|
 | c1567    256     4      |  18     137     13678   |  9       3567    236      |
 |  8       2569    2567   |  49     3479    3679    |  24567   1       2346     |
 | c1679    3       167    |  5     d1479    2       |  4678    4678    46       |
 *-------------------------------------------------------------------------------*

If r5c46 is not 2, but 19, there are hidden pairs 19 in c19, 9 goes to r1c9 and r9c1, and 1 to r3c9 and r7c1, forcing 1 both to r1c5 and r9c5 => 2r5c4

Code: Select all

 *------------------------------------------------------------------------*
 |  46      468    3     |  7     149    5      |  1468   2       1469    |
 |  47      1      2     | #489   6      3      |  478    4789    5       |
 |  4567    4568   9     | #148   2     #18     |  3      4678    146     |
 |-----------------------+----------------------+-------------------------|
 |  2       569    8     |  3     159    4      |  156    569     7       |
 |  14569   7      156   |  2     8      19     |  1456   34569   13469   |
 |  3       459    15    |  6     1579   179    |  2      459     8       |
 |-----------------------+----------------------+-------------------------|
 |  156     256    4     |  18    137    1678   |  9      3567    236     |
 |  8       2569   567   | #49    3479   679    |  4567   1       2346    |
 |  169     3      167   |  5     1479   2      |  4678   4678    46      |
 *------------------------------------------------------------------------*

4 digits in 4 cells, none can be twice => 1r3c46 => -1r3c9, bte

[jovi_al01]

one of my fastest solves from you in a while, just about five minutes for me
thank you for the great puzzle!

Code: Select all

.--------------------.--------------------.----------------------.
| 46     468    368  | 7    #*1349  5     |*1468   2     #1469   |
| 47     1      2378 | 2489  6      389   | 478    4789   5      |
| 4567   24568  9    | 1248  124    18    | 3      4678  *146    |
:--------------------+--------------------+----------------------:
| 2      5689   1568 | 3    a159    4     | 156    569    7      |
|#*14569 7      156  |a129   8     a19    | 12456  34569 #*123469|
| 3      459    15   | 6    a12579 [179]  | 1245   459    8      |
:--------------------+--------------------+----------------------:
|*1567   256    4    | 18    137    13678 | 9      3567   236    |
| 8      2569   2567 | 49    3479   3679  | 24567  1      2346   |
|#1679   3     *167  | 5    #*1479  2     | 4678   4678   46     |
'--------------------'--------------------'----------------------'

bilocals on 9s marked in #s
suppose 9 is in r1c9 and r9c1.
a cycle on 1s (*) then eliminates all of 1 from b5p2468 (a), placing it in r6c6.
suppose then, that 9 is only in one of r1c9 and r9c1. it must then be placed in r5 and c5 somewhere in r19c19. this eliminates 9 from all of b5p2468.
in either case, r6c6 is 1 or 9. this collapses the puzzle to basics.

apologies if i missed something, or explained it in a non-elegant way. it at least felt intentionally placed!
edit: fixed some typos

[yzfwsf]

Even reading these chains is hard, unless you click on the digits in a solver, because you don't even know, which one you should remember and erase it in your mind in the 3 units. Have you tried that without solver ?

Sorry, this one is purely a computer solution, I'm an extremely poor manual solver. I will be less involved in puzzle solutions in the future so as not to disturb good manual solvers like you.

[P.O.]

this puzzle is in 3-template and is solved by considering the combination (1 7 9) which has 105 instances which all have in common n7r6c5

Hidden Text: Show

Code: Select all

initialization:
#VT: (46 6 6 60 16 107 18 16 11)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil (62) nil

46      468     368     7       1349    5       1468    2       1469             
47      1       2378    2489    6       389     478     4789    5               
4567    24568   9       1248    124     18      3       4678    146             
2       5689    1568    3       159     4       156     569     7               
14569   7       156     129     8       19      12456   34569   123469           
3       459     15      6       12579   179     1245    459     8               
1567    256     4       18      137     13678   9       3567    236             
8       2569    2567    49      3479    3679    24567   1       2346             
1679    3       167     5       1479    2       4678    4678    46               


1: (1 7 9)
#VT: (14 6 6 60 16 107 7 16 8)
Cells: nil nil nil nil nil nil (50) nil nil
SetVC: ( n7r6c5   n2r6c7   n2r5c4   n2r3c5   n5r4c5   n2r2c3
         n3r2c6   n3r1c3   n8r4c3   n1r4c7 )

#VT: (8 2 3 60 6 107 6 6 8)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:(24 60) nil nil nil (37) nil (55 73) nil nil
EraseCC: ( n8r3c6   n8r7c4   n8r1c2   n1r3c4   n1r1c9   n9r5c9
           n9r2c8   n9r1c5   n4r2c4   n6r4c8   n1r5c6   n9r6c6
           n9r8c4   n7r2c1   n8r2c7   n9r4c2   n1r6c3   n3r5c8
           n7r3c8   n8r9c8   n9r9c1   n5r7c8   n4r6c8   n5r5c7
           n5r6c2   n6r5c3   n7r9c3   n4r5c1   n5r8c3   n6r1c1
           n4r1c7   n5r3c1   n4r3c2   n6r3c9   n1r7c1   n3r7c5
           n2r7c9   n4r8c5   n3r8c9   n1r9c5   n6r9c7   n4r9c9
           n6r7c2   n7r7c6   n2r8c2   n6r8c6   n7r8c7 )
6 8 3   7 9 5   4 2 1
7 1 2   4 6 3   8 9 5
5 4 9   1 2 8   3 7 6
2 9 8   3 5 4   1 6 7
4 7 6   2 8 1   5 3 9
3 5 1   6 7 9   2 4 8
1 6 4   8 3 7   9 5 2
8 2 5   9 4 6   7 1 3
9 3 7   5 1 2   6 8 4


[totuan]

Code: Select all

 *-----------------------------------------------------------------------------*
 |&46      468     368     | 7       1349    5       | 1468    2      #1469    |
 |&47      1       2378    |%2489    6       389     | 478     4789    5       |
 |&4567    24568   9       |%1248    124    %18      | 3       4678   *146     |
 |-------------------------+-------------------------+-------------------------|
 | 2       5689    1568    | 3       159     4       | 156     569     7       |
 |#14569   7       156     |@129     8      @19      | 12456   34569  #123469  |
 | 3       459     15      | 6       12579   179     | 1245    459     8       |
 |-------------------------+-------------------------+-------------------------|
 |*1-567   256     4       | 18      137     13678   | 9       3567    236     |
 | 8       2569    2567    |%49      3479    3679    | 24567   1       2346    |
 |#1679    3       167     | 5       1479    2       | 4678    4678    46      |
 *-----------------------------------------------------------------------------*

My path for this one: Look at (19)r5c6 and bilocate 9’s c19 => (1)r7c1=(1)r3c9

(1)r7c1=(18)r3c69-(18=249)r238c4-(29=19)r5c46-(19=4567)r1235c1 => r7c1<>567, stte

Thanks for the puzzle!
totuan

[eleven]

Sorry, this one is purely a computer solution, I'm an extremely poor manual solver. I will be less involved in puzzle solutions in the future so as not to disturb good manual solvers like you.

yz, i am sorry, if you felt offended in any way, my post was just a quick reaction, because the nodes to remember are not marked for better readability, as i am used from (extended) AIC chains. Different to the hardest thread, which in my eyes is contributed to manual solver hardness, i also think, that this one should be open to solutions of all kinds. There are other readers, who are primarily interested in computer solutions, and of course manual players also can learn from them.

[Cenoman]

Code: Select all

 +-------------------------+-------------------------+---------------------------+
 |  46      468     368    |  7      349-1   5       |  1468    2       19       |
 |  47      1       2378   |  2489   6       39      |  478     4789    5        |
 |  4567    24568   9      | #1248   24-1   #18      |  3       4678    146      |
 +-------------------------+-------------------------+---------------------------+
 |  2       5689    168    |  3      159     4       |  156     569     7        |
 |Db14569   7       156    |Ed129    8      c19      |  12456   34569   123469   |
 |  3       459     15     |  6      12579   179     |  1245    459     8        |
 +-------------------------+-------------------------+---------------------------+
 | C1567    256     4      | #18     137    #13678   |  9       3567    236      |
 |  8       2569    2567   |  49     3479    3679    |  24567   1       236      |
 |Ba19      3      A167    |  5     z1479    2       |  4678    4678    46       |
 +-------------------------+-------------------------+---------------------------+

Kraken row (1)r9c135 & almost M2-Wing (#):

Code: Select all

(1-9)r9c1 = r5c1 - (9=1)r5c6
 ||                         \
 ||                        (1)r5c4 = [(1)r3c4 = (1-8)r7c4 = r7c6 - (8=1)r3c6] *
 ||                         /
(1)r9c3 - r79c1 = (1)r5c1 -
 ||
(1)r9c5 *
----------
=> -1 r13c5; lclste

or

Hidden Text: Show

as a chain:
[(1=8)r3c6 - r7c6 = (8-1)r7c4 = (1)r3c4] = (1)r5c4 - [(1=9)r5c6 - r5c1 = (9-1)r9c1 *=* r9c3 - r79c1 = r5c1] = (1)r9c5 => -1 r13c5; lclste

[shye]

thank you for your many wonderful solutions!

what i initially aimed to make was the following:

Code: Select all

.---------------------.----------------------.-----------------------.
|  46     468    368  | 7    #C1349    5     |C1468   2      #1469   |
|  47     1      2378 | 2489   6       389   | 478    4789    5      |
|  4567   24568  9    | 1248   124     18    | 3      4678   C146    |
:---------------------+----------------------+-----------------------:
|  2      5689   1568 | 3     *159     4     | 156    569     7      |
|#C14569  7      156  |*129    8      *19    | 12456  34569 #C123469 |
|  3      459    15   | 6     *12579  #19-7  | 1245   459     8      |
:---------------------+----------------------+-----------------------:
| C1567   256    4    | 18     137     13678 | 9      35678   236    |
|  8      2569   2567 | 49     3479    3679  | 24567  1       2346   |
| #1679   3     C167  | 5    #C1479    2     | 4678   4678    46     |
'---------------------'----------------------'-----------------------'

9r1c9 = 9r1c5 & 9r5c9 - 9b5p2468 = 9b5p9
9r9c1 = 9r5c1 & 9r9c5 - 9b5p2468 = 9b5p9
therefore
9b5p9 == (9-1)r1c9 & r9c1 = [CNL: 1r1c5 = r1c7 - r3c9 = r5c9 - r5c1 = r7c1 - r9c3 = r9c5 - r1c5 loop] - 1b5p2468 = 1b5p9
=> -7b5p9 lcstte

since this is also a loop because of the weak link from 1 to 9 in b5p9, there are a lot of additional eliminations, but theyre not any more useful
=> -46r1c9, -67r9c1, -1r37c5, -1r5c37

the T&L representation covers these extra elims

XSudo Input: Show

10 Truths = {1R19 9R19 1C19 9C19 19B5}
9 Links = {19r5 19c5 9n1 6n6 1n9 1b37}

here is another solution i found later, inspired by all of your responses (particularly, eleven and ttt)

(1=9)r5c6 - 9r5c1&r5c9 = (9-1)r1c9&r9c1 = [swordfish: 1s in c149 covered by r357] - 1r5c6 loop
=> -9r5c48, -46r1c9, -67r9c1, -1r3c56, -1r5c37, -1r7c56 stte

XSudo Input: Show

6 Truths = {1C149 9C19 5N6}
6 Links = {1r357 9r5 9n1 1n9}

effective eliminations for stte: -1r3c6, -9r5c4, -1r7c56