The New Sudoku Players' Forum

[Mauriès Robert]

Hi,
Here is a new puzzle to solve.
.4..8..6...5.4.9.....1.3...2.......4.372.468.6.......1...8.5.....1.9.3...7..3..9.
Good sudoku
Robert

puzzle: Show

[totuan]

Hi All,
Robert’s puzzles 2019-12-06
After basic SSTS:

Code: Select all

 *--------------------------------------------------------------------*
 | 137    4      23     | 59     8      279    | 1257   6      2357   |
 | 1378   1268   5      | 67     4      267    | 9      127    2378   |
 | 789    2689   2689   | 1      2567   3      | 24578  2457   2578   |
 |----------------------+----------------------+----------------------|
 | 2      1589   89     | 359    1567   16789  | 57     357    4      |
 | 15     3      7      | 2      15     4      | 6      8      9      |
 | 6      589    4      | 359    57     789    | 257    2357   1      |
 |----------------------+----------------------+----------------------|
 | 349    269    2369   | 8      1267   5      | 1247   1247   267    |
 | 458    2568   1      | 467    9      267    | 3      2457   25678  |
 | 458    7      268    | 46     3      126    | 12458  9      2568   |
 *--------------------------------------------------------------------*

My ugly path for this one ER9.0, hope a better from others – not hard but long…

01- (1)r9c6=r9c7-r1c7=r1c1-r5c1=r5c5 => r7c5<>1, r9c6=1
02- Present as diagram: => r1c4<>9, r1c4=5, r1c6=9

Code: Select all

AUR(35)r46c48
 ||
(9)r46c4*
 ||
(5)r8c8-r8c12=r9c1-r5c1=r5c5--r3c5=r1c4*
 ||                          |
(5)r3c8----------------------

03- Present as diagram: => r3c5<>7

Code: Select all

(5)r8c89-r8c12=r9c1-r5c1=r5c5-(5=7)r6c5*
 ||
(5)r9c9-r3c9=(45-8)r3c78=(8)r9c7-(8)r9c1
 ||    |                          ||
 ||    |                         (4)r9c1-(4=6)r9c4-(6=7)r2c4*
 ||    |                          ||
 ||     -------------------------(5)r9c1
 ||
 ||                              (6)r2c2-(6=7)r2c4*
 ||                               ||
(5)r9c7-(5=7)r4c7-(7)r6c7        (2)r2c2-r2c6=r3c5*
                   ||             ||
                  (7)r6c5)*      (1)r2c2-r12c1=r5c1-(1=5)r5c5-(5=7)r6c5*
                   ||             ||
                  (7-8)r6c6=r6c2-(8)r2c2

04- (2=1)r2c8-(1)r1c7=(1-7)r1c1=(7-9)r3c1=(9-3)r7c1=r7c3-(3=2)r1c3 => r1c79<>2, some singles
05- Present as diagram: r1c7<>7, some single

Code: Select all

(5)r8c89-r8c12=r9c1-(5=1)r5c1-r1c1=r1c7*
 ||
(5)r9c7-(5=7)r4c7*
 ||
(5-2)r9c9=r9c7-(2=57)r46c7*

06- (8)r6c6=r6c2-(8=1)r2c2-r4c2=(1-6)r4c5=r4c6 => r4c6<>8, r6c6=8
07- (7)r7c9=r7c5-r6c5=r6c8 => r8c8<>7, stte

totuan

[Mauriès Robert]

With TDP you can make a quick resolution as soon as you accept the principle of contradiction, for example with 1b1 (see here). But as it is not the spirit on this forum, here is a resolution by TDP with short chains that mainly use Th2 TDP part 1 (anti-track P'), Th2 TDP part 2 (conjugated tracks P) and TDP part 4 (extension).
I recall my notation: {a, b, c, ...} means a => b=> c, etc...
1) P'(1r5c5) = {1r5c1, 1r2c2, 1r7c8, 1r9c6, ...} => -1r4c6 => r9c6=1.

2) P'(2r1c3) = {3r1c3, 3r7c1, 3r2c9, 9r3c1, 8r3c79, 26r3c23, ...} => -2r2c2

3) P'(5r8c2) = {5r89c1, 1r5c1, 1r2c2, 1r4c4, 6r3c23, 6r7c5, 2r8c6, ...} => -2r8c2
=> X-wing 2c2c5 => -2r3c3, -2r3c789, -2r7c3, -2r7c789

4) P'(7r7c5).P(2r7c5) = {2r7c5, 2r9c3, 3r1c3, 69r7c23, 7r7c9, ...} et P'(7r7c5).P(6r7c5) = {6r7c5, 7r7c9, ...} => -7r7c78 => -4r7c1 -4r8c8, -4r9c7

5) P(6r4c6) = {6r4c6, 8r6c6, ...} et P(6r4c5) = {6r4c5, 1r5c5, 5r5c1, 48r89c1, ...} which is developed by an extension:
P(6r4c5).P(2r9c3) = {..., 2r9c3, 3r1c3, 3r2c9, 8r3c79, 8r2c2, 8r6c6, ...}
P(6r4c5).P(6r9c3) = {..., 6r9c3, 4r9c4, 8r9c1, 8r8c9, 8r3c7, 8r2c2, 8r6c6, ... }
=> r6c6=8

6) P(2r1c3) = {2r1c3, 2r3c5, 2r7c2, 3r7C3,...} et P(3r1c3) = {3r1c3, 3r2c9, 3r7c1, 9r3c1, 8r2c79, 6r3c3, 9r7c3...}
= > -6r7c3, -9r7c2 et -6r3c5 => -6r2c2

7) P(9r6c2) = {5r6c2, 1r5c1, 1r4c5, 6r7c5, 2r7c2, 4r9c4, 5r9c1,..., 7r6c5, 2r6c7, 8r9c7, 6r9c3, 6r3c2, ...}
=> -9r3c2 => r4c3=8, -6r8c2, -8r3c2

8) P(1r5c5) = {1r5c5, 5r5c1, 5r8c2, ...} et P(5r5c5) = {5r5c5, 7r6c5, 2r3c5, 2r8c6, ..., 7r7c9, 5r8c8, ...}
=> -5r8c19

9) P'(9r1c6) = {9r1c4, 5r3c5, 1r5c5, 5r5c1, 5r8c2, ..., 7r6c5, 7r7c9, 8r3c9, 8r9c7, 4r9c1, 6r9c4, 7r2c4, ...} => -7r1c6

10) P(5r3c8)={5r3c8, 5r1c4, 9r1c6, ...}, P(5r8c8) = {5r8c8, 5r9c1, 5r5c5, 5r1c4, 9r1c6, ...} et
P(5r46c8) = {5r46c8, 2r6c7, 7r6c5, 7r7c9, 2r8c8, 2r7c5, 2r9c3, 3r1c3, 3r2c9, 2r1c9, ...} => -2r1c6
=> r1c6= 9, r1c4=5
Note: the use of UR35r46c48 has been deliberately avoided here, allowing the same result to be achieved more quickly, in order to preserve the proof of the uniqueness of the solution.

11) P(2r1c3) = {2r1c3, 6r9c3, 4r9c4, ...} et P(2r3c2) = {2r3c2, 2r2c6, 6r2c4, 4r9c4,...} => r9c4=4 =>r8c1=4

12) P(5r9c1) = {5r9c1, 1r5c1, 1r2c2, ...} et P(8r9c1) = {8r9c1, 8r2c2, 257r469c7, 1r1c7, 1r2c1, ...} => -1r2c8
=> r1c7=1, r7c7=4, r7c8=1, r3c8=4, -7r2c19, -2r2c9
But also
P(5r9c1) = {5r9c1, 1r5c1, 5r5c5, 7r6c5, ...} et P(8r9c1) = {8r9c1, 5r8c2, 8r3c7, 5r3c9, 5r9c7, 7r4c7,...} => -5r9c9 , -7r6c78 => r6c5=7 and fine with singles.
Robert

[SpAce]

Hi Robert,

Unfortunately I haven't had time to look at these puzzles of yours, but it's good to know both totuan and you (previously others too) have provided some reference resolutions. There hasn't been much solving activity in harder puzzles on this forum lately, so I'm glad that you've rekindled interest in that. Looks like totuan likes it too (which is great because we all love his clever solutions and diagrams )! Thus, don't take it as lack of interest if you receive few responses.

Just a quick comment about this:

I recall my notation: {a, b, c, ...} means a => b=> c, etc...

I'd like to remind that the latter (implication chain) notation has no memory, so such simple mapping only works if building the {a,b,c...} set doesn't require a net. Your notation doesn't distinguish between chains and nets, so it's impossible to know. That's something you might want to think about, because a net implies more complexity than a linear chain, and we generally like to have an idea how complex a move is. That information is hidden in your system.

[Cenoman]

My ugly path for this one ER9.0, hope a better from others – not hard but long…

I had a first path in 13 steps or so. It was more than ugly, and if totuan's is long, how to qualify mine ?
I post to day, first to congratulate totuan for his very efficient and elegant path.
His expectation of a better one will be disappointed.
I just wanted to draw attention upon his key move at step 2 (UR 35r46c48). I have read recent exchanges denying the legitimacy of uniqueness techniques. This puzzle is a nice example of a path drastically shortened by the use of these. I had missed it
Here is just another way to use it:

Code: Select all

 +-----------------------+-----------------------+-------------------------+
 |  137    4      23     |  59    8      279     |  1257    6      2357    |
 |  1378   1268   5      |  67    4      267     |  9       127    2378    |
 |  789    2689   2689   |  1     2567   3       |  24578   2457   2578    |
 +-----------------------+-----------------------+-------------------------+
 |  2      1589   89     |  359   1567   16789   |  57      357    4       |
 |  15     3      7      |  2     15     4       |  6       8      9       |
 |  6      589    4      |  359   57     789     |  257     2357   1       |
 +-----------------------+-----------------------+-------------------------+
 |  349    269    2369   |  8     1267   5       |  1247    1247   267     |
 |  458    2568   1      |  467   9      267     |  3       2457   25678   |
 |  458    7      268    |  46    3      126     |  12458   9      2568    |
 +-----------------------+-----------------------+-------------------------+

1. (1)r5c5=r5c1-r1c1=r1c7-r9c7=(1)r9c6 =>-1r7c5; one placement
2. UR(35)r46c48 using mixed internals-externals (borrowed to totuan)
(9)r46c4
(5)r3c8-r3c5=(5)r1c4
(5)r8c8-r8c12=r9c1-r5c1=r5c5-r3c5=(5)r1c4
=>-9r1c4; two placements

Code: Select all

 +-----------------------+---------------------+-------------------------+
 |  137    4      23     |  5     8      9     |  127     6      237     |
 |  1378   1268   5      |  67    4      267   |  9       127    2378    |
 |  789    2689   2689   |  1     267    3     |  24578   2457   2578    |
 +-----------------------+---------------------+-------------------------+
 |  2      1589   89     |  39    1567   678   |  57      357    4       |
 |  15     3      7      |  2     15     4     |  6       8      9       |
 |  6      589    4      |  39    57     78    |  257     2357   1       |
 +-----------------------+---------------------+-------------------------+
 |  349    269    2369   |  8     267    5     |  1247    1247   267     |
 |  458    2568   1      |  467   9      267   |  3       2457   25678   |
 |  458    7      268    |  46    3      1     |  2458    9      2568    |
 +-----------------------+---------------------+-------------------------+

3. Kraken column (6)r347c5
(6)r3c5-r2c46=(6-1)r2c2=(1-895)b4p238=(5)r8c2
(6-1)r4c5=(1-895)b4p238=(5)r8c2
(6-2)r7c5=(2)r8c6
=>-2r8c2

4. Multi krakens, presented as a net:

Code: Select all

(6)r4c6-(6=157)r456c5- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 ||                                                                                   |
                  (5)r9c9-r3c9=(5-48)r3c78=(8)r9c7    (4)r9c1-r9c4=(4-7)r8c4=(7)r2c4  | (7)r3c789-(7=123)b3p135*
 ||                ||                            \     ||                        \    |  ||
(7)r4c6-(7=5)r4c7-(5)r9c7                         ---(8)r9c1                      -----(7)r3c5
 ||                ||                            /     ||                        /       ||
                  (5)r9c1- - - - - - - - - - - -      (5)r9c1-r5c1=r5c5-(5=7)r6c5       (7-93)r37c1=(3)r7c3*     
 ||           
      (8)r6c6=r6c2- - - - - - - - (8)r2c2
 ||   /                            ||
(8)r4c6                           (8-3)r2c9=(3)r1c9*
      \                            ||
      (8=571)b5p589-(1=458)r589c1-(8)r2c1
-------------
=> -3 r1c3; six placements

Code: Select all

 +--------------------+---------------------+-----------------------+
 |  137   4      2    |  5     8      9     |  17     6      37     |
 |  138   18     5    |  67    4      67    |  9      12     238    |
 |  78    69     69   |  1     2      3     |  4578   457    578    |
 +--------------------+---------------------+-----------------------+
 |  2     1589   89   |  39    1567   678   |  57     357    4      |
 |  15    3      7    |  2     15     4     |  6      8      9      |
 |  6     589    4    |  39    57     78    |  257    2357   1      |
 +--------------------+---------------------+-----------------------+
 |  9     2      3    |  8     67     5     |  14     14     67     |
 |  458   568    1    |  467   9      2     |  3      57     5678   |
 |  458   7      68   |  46    3      1     |  258    9      2568   |
 +--------------------+---------------------+-----------------------+

5. Kraken row (7)r6c5678
||(7)r6c5-r7c5=(7)r7c9
||(7-8)r6c6=r6c2-(8=1)r2c2-r4c2=(1-6)r4c5=r7c5-(6=7)r7c9
||(7-2)r6c7=r6c8-(2=17)b3p15-r13c9=(7)r78c9
||(7)r6c8
=> -7 r8c8; ste

[totuan]

Hi Cenoman and All,

My ugly path for this one ER9.0, hope a better from others – not hard but long…

I had a first path in 13 steps or so. It was more than ugly, and if totuan's is long, how to qualify mine ?

His expectation of a better one will be disappointed.

I think you should not care much about that, it's been my bad habit when I post solutions on sudoku forums for a long time, I'm hard to change it... I'm so sorry.
I'm happy to see many of you still here, hopefully abi (Shophie - maybe like me, she is hard to cure the sudoku addiction... ) and others can arrange a time to join with us.

Thanks to All and have a nice weekend!
totuan