The New Sudoku Players' Forum

[yzfwsf]

Code: Select all

9..2....4....6......3..4.5.2.........3.72...6..5..94....2.3...76.....8...7.4...9.

SE:8.5/Hoduku Rate:22398/YZF_SUDOKU Rate:14820

[totuan]

My path for this one – quite long path for puzzle with ER8.5, at first I considered AUR(37)r12c67 so my path has followed that:
After basic SSTS:

Code: Select all

 *--------------------------------------------------------------------*
 | 9      1568   1678   | 2      1578   13578  | 1367   13678  4      |
 | 14578  12458  1478   | 13589  6      13578  | 12379  12378  12389  |
 | 178    1268   3      | 189    1789   4      | 12679  5      1289   |
 |----------------------+----------------------+----------------------|
 | 2      1689   16789  | 13568  4      13568  | 13579  1378   13589  |
 | 148    3      1489   | 7      2      158    | 159    18     6      |
 | 178    168    5      | 1368   18     9      | 4      12378  1238   |
 |----------------------+----------------------+----------------------|
 | 1458   14589  2      | 15689  3      1568   | 156    146    7      |
 | 6      1459   149    | 159    1579   1257   | 8      1234   1235   |
 | 3      7      18     | 4      158    12568  | 1256   9      125    |
 *--------------------------------------------------------------------*

01: (X-wing 3’s: r68c89)=(3-6)r6c4=r6c2-r3c2=r3c7-r1c8=(6-4)r7c8=(4-3)r8c8=r8c9 => r24c9<>3
02: Present as diagram: => r2c8<>3

Code: Select all

(2-4)r8c8=(4-6)r7c8=r1c8----------------------------
 ||                                                 |
(2-7)r6c8=r6c1-(7)r3c1                              |
 ||             ||                                  |
 ||            (7)r3c5-r8c5=(7-2)r8c6=(2-6)r9c6=r9c7-r3c7=r3c2-r6c2=(6-3)r6c4=r4c46-r4c7=r12c7*
 ||             ||                                  |
(2)r2c8*       (7)r3c7------------------------------

03: Present as diagram: => r1c7<>6

Code: Select all

(3)r6c8-(2)r6c8
 ||      || 
 ||     (2)r2c8-r2c2=(2-6)r3c2=r3c7*
 ||      ||
 ||     (2-4)r8c8=(4-6)r7c8=r1c8*
 ||
(3-6)r6c4=r6c2-r3c2=r3c7*
 ||
(3)r6c9-r8c9=(3-4)r8c8=(4-6)r7c8=r1c8*

04: (6)r6c4=r6c2-r3c2=r3c7-r9c7=r9c6 => r4c6<>6
05: Present as diagram: => r7c7<>5

Code: Select all

(X-wing 5’s: r27c14)*
 ||                       
(5)r8c4-r8c2=r7c12*
 ||
(5)r4c4-r4c9=r89c9*

06: Present as diagram: => r1c8<>3 => r4c7<>3

Code: Select all

(3)r1c7*    AALS(13578)r145c6
 ||           ||     
(7)r1c7------(7)r1c6
 ||           || 
 ||          (158)r145c6-(158=6)r7c6-r7c8=r1c8*
 ||           ||
 ||          (3)r4c6-r4c7=r12c7*       
 ||           ||
 ||          (3)r1c6*
 ||
(1)r1c7-(1=6)r7c7-r7c8=r1c8*

07: Present as diagram: => r6c1<>18, r6c1=7

Code: Select all

AUR(37)r12c67
 ||                               
(3)r4c6-(3=168)r6c245*
 ||                         
(7-2)r8c6=(2-6)r9c6=r9c7-r3c7=r3c2-(6=18)r6c25*
 ||                     |
(7)r3c7-----------------
 ||
(7)r4c7-r4c3=r6c1*

From here the puzzle become quite easy, one of simple as below:

08: (6)r9c7=(6-2)r9c6=(2-7)r8c6=r8c5-r3c5=r3c7 => r3c7<>6, some singles
09: UR(23)r68c89 => r8c9<>23, some singles
10: (8)r6c2=r6c5-r9c5=r9c3 => r5c3<>8
11: (1=8)r5c9-(9=8)r4c9-r4c2=r5c3 => r5c3<>1
12: (5)r1c2=(5-9)r7c2=r4c2-(9=4)r5c3-r2c3=r2c2 => r2c1<>5, stte

totuan

[Ajò Dimonios]

Code: Select all

+-------------------+------------------+-------------------+
| 9     1568  1678  | 2     1578 13578 | 1367  13678 4     |
| 14578 12458 1478  | 13589 6    13578 | 12379 12378 12389 |
| 178   1268  3     | 189   1789 4     | 12679 5     1289  |
+-------------------+------------------+-------------------+
| 2     1689  16789 | 13568 4    13568 | 13579 1378  13589 |
| 148   3     1489  | 7     2    158   | 159   18    6     |
| 178   168   5     | 1368  18   9     | 4     12378 1238  |
+-------------------+------------------+-------------------+
| 1458  14589 2     | 15689 3    1568  | 156   146   7     |
| 6     1459  149   | 159   1579 1257  | 8     1234  1235  |
| 3     7     18    | 4     158  12568 | 1256  9     125   |
+-------------------+------------------+-------------------+


P(6r9c7)=>contradiction=>-6r9c7+6r9c6+2r8c6+7r8c5+9r3c5
P(2r9c9)=>cobtradiction=>-2r9c9+2r9c7
P(8r7c1)=>contradiction=>-8r7c1
P(8r7c2)=>contradiction=>-8r7c2+8r9c3
P(8r1c2)=>contradiction=>-8r1c2
P(8r1c6)=>contradiction=>-8r1c6
P(8r1c8)=>contradiction=>-8r1c8+8r1c5+5r9c5+1r9c9+1r6c5+1r3c4+1r7c6+8r7c4+9r7c2+9r8c4
P(3r2c4)=>contradiction=>stte

[totuan]

By “style of contradiction”, then the presenting of solution for all puzzles become very easy
An example for this one:
P(6r3c7) => contradiction => -6r3c7, many singles
P(5r2c1) => contradiction => -5r2c1, stte

totuan

[Ajò Dimonios]

The track P (6L3C7) does not produce contradiction using only the basic technique. To use TDP you only need to use the basic technique.

Paolo

[totuan]

The track P (6L3C7) does not produce contradiction using only the basic technique. To use TDP you only need to use the basic technique.

Aha…! Ok, just for fun:
P(5r7c7) => contradiction => -5r7c7
P(6r3c7) => contradiction by UR(37)r12c67 => -6r3c7, many singles
P(5r2c1) => contradiction => -5r2c1, stte

In fact, I just want to say: if TDP presents such solutions, it seems like T&E, no more information for readers - no need to spend time studying Advanced solving Techniques and SK–loop, Exocet…
What a pity !!!

totuan

[Mauriès Robert]

In fact, I just want to say: if TDP presents such solutions, it seems like T&E, no more information for readers - no need to spend time studying Advanced solving Techniques and SK–loop, Exocet…

No Totuan, the resolution given by Paolo, without details explaining his choices, is not representative of the TDP which is not reducible to T&E.
I know that on this forum we do not like to talk about invalidity or contradiction, and yet the contradiction is present in many of the proposed resolutions with AICs that are often chains of contradiction.
I think that Paolo wanted to show the fastest resolution, and this is achieved by looking for invalid leads, but this is not T&E, because the candidates chosen are not taken at random.
Sincerely
Robert

[Ajò Dimonios]

Hi Robert, Hi Totuan:

I agree with Robert I have reported in a simplified way the contradictions obtained with the TDP. I think that apart from the multiple elimination techniques like MSLS, SKloop, Exocet etc ... all the other advanced techniques with single elimination are nothing more than contradiction techniques that use the language of the basic technique. If I am allowed to make a comparison, the basic technique represents the basic rules of algebra and the advanced techniques are nothing more than some of the algebraic expressions that can be obtained using algebra. Every particular contradiction is obtained with a complex algebraic expression. Surely someone on this site and in that of Robert https://www.assistant-sudoku.com/ will be able to obtain a lower number of 8 contradictions to solve this scheme.

Paolo

[Mauriès Robert]

Hi Totuan,
To continue my previous explanations, here is on this puzzle a solving operation which is the true face of TDP.
As we can see the hidden UR(23)r6b6-r8b9, we can say that for the set E={3r4b6, 2r9b9} the anti-track P'(E) is invalid. This can be verified directly also by building the anti-track.
From then on, it is possible to say that the tracks P(3r4b6) and P(2r9b9) are conjugated.
So I draw on the puzzle (see image1 below) these two tracks, one in blue the other in yellow to study their interactions from which I deduce: r8c5=7, r3c5=9 and r8c6=2.
But the "intelligent" search for contradiction is also part of the TDP.

image1: Show

I continue with the pair 2r9b9 which has just appeared with these placements, by an anti-track (see image2):
P'(2r9c7): -2r9c7->2r9c9->18r3c49->7r3c1->7r4c3->6r1c3->6r3c7 => -6r9c7.

image2: Show

If I find time to continue this resolution, I will add it here.
Sincerely
Robert

[totuan]

Hi Robert,

To continue my previous explanations, here is on this puzzle a solving operation which is the true face of TDP.
As we can see the hidden UR(23)r6b6-r8b9, we can say that for the set E={3r4b6, 2r9b9} the anti-track P'(E) is invalid. This can be verified directly also by building the anti-track.
From then on, it is possible to say that the tracks P(3r4b6) and P(2r9b9) are conjugated.
So I draw on the puzzle (see image below) these two tracks, one in blue the other in yellow to study their interactions from which I deduce: r8c5=7, r3c5=9 and r8c6=2.

Thanks for explanation.
I have known that path, it's easy to write as AIC:
AUR(23)r67c89[(2)r8c6=(3)r6c4]-(6)r6c4=r6c2-r3c2=r3c7-r9c7=r9c6 => r9c6<>2, r8c6=2, r8c5=7, r3c5=9
then
(2)r3c9=(26-7)r3c27=r3c1-r6c1=(7-2)r6c8=r6c9 => r9c9<>2, r9c7=2, r9c6=6

But from here this one is still long & hard to finish - [Edited] using presentation solution style on this forum (need more detail and information for per steps), at least for me

totuan

[Mauriès Robert]

Hi Tetouan,
What are this rules on this forum, other than writing in English, not using insulting language and being courteous?
Robert

[eleven]

This indeed is a "normal" move needing no complex net, as you achieve it with the trying of alternative paths. So i would not call it the true face of TDP.
2r8c6 =UR23r49c79= (3-6)r6c4 = r6c2 - r3c2 = r3c7 - r1c8 = (6-4)r7c8 = (4-23)r8c8 = 23r8c69 => 2r8c6
However it does not make the puzzle much easier.
[cross posted with totuan]

[Mauriès Robert]

Hi Eleven,
Vous écrivez :

This indeed is a "normal" move needing no complex net, as you achieve it with the trying of alternative paths. So i would not call it the true face of TDP.
2r8c6 =UR23r49c79= (3-6)r6c4 = r6c2 - r3c2 = r3c7 - r1c8 = (6-4)r7c8 = (4-23)r8c8 = 23r8c69 => 2r8c6

What do you know about TDP as I understand it to say that !
Here I show Tetouan that TDP understands a lot of things and that it can't be reduced to T&E :
AIC channels are nothing but invalid anti-tracks. Your chain is the anti-track P'(2r8c6), I could have treated the 2r8c6 validation this way.
Berthier's whips are equivalent to invalid tracks from the target, etc...
I note that your interventions in response to my comments are often to denigrate TDP. What are you looking for ? What are your intentions ?
Robert

[totuan]

Hi Robert,

What are this rules on this forum, other than writing in English, not using insulting language and being courteous?

I'm sorry for using wrong word in English - I edited.

totuan

[eleven]

What are you looking for ? What are your intentions ?

I am an admirer of the "Art of Sudoku Solving", as it has been practised by RW, SteveK, MythJellies, ..., David Bird and totuan. It is characterized by nice ideas showing the beauty and variety of puzzles, and therefore including many techniques, they developed through their insight of sudoku properties. Not missing a plan (which might change through the solving process), how to effectively crack a puzzle.
The opposite is backtracking, the most effective way of solving puzzles with a program.
Systems like TDP or Resolution Rules are between these approaches, and for my taste too mechanical. This does not change much, when other ideas (like uniqueness) are integrated.