The New Sudoku Players' Forum

[denis_berthier]

.
Same pattern as "anti-radiations2 7.2", but for those who prefer harder puzzles.
This puzzle is minimal.

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+-------+-------+-------+
! . . 9 ! . . . ! 6 . . !
! . 6 . ! 2 3 8 ! . 5 . !
! 3 . . ! . . . ! . . 7 !
+-------+-------+-------+
! . 1 . ! . 8 . ! . 6 . !
! . 3 . ! 5 . 1 ! . 9 . !
! . 7 . ! . 9 . ! . 1 . !
+-------+-------+-------+
! 1 . . ! . . . ! . . 5 !
! . 9 . ! 7 2 5 ! . 8 . !
! . . 8 ! . . . ! 2 . . !
+-------+-------+-------+
..9...6...6.238.5.3.......7.1..8..6..3.5.1.9..7..9..1.1.......5.9.725.8...8...2.. # 95908 FNBYK C28.m/S8.f
SER = 8.3

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Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 245   2458  9     ! 14    1457  47    ! 6     234   1348  !
   ! 47    6     147   ! 2     3     8     ! 149   5     149   !
   ! 3     2458  1245  ! 1469  1456  469   ! 148   24    7     !
   +-------------------+-------------------+-------------------+
   ! 9     1     245   ! 34    8     2347  ! 3457  6     234   !
   ! 2468  3     246   ! 5     467   1     ! 478   9     248   !
   ! 24568 7     2456  ! 346   9     2346  ! 3458  1     2348  !
   +-------------------+-------------------+-------------------+
   ! 1     24    23467 ! 8     46    3469  ! 349   347   5     !
   ! 46    9     346   ! 7     2     5     ! 134   8     1346  !
   ! 4567  45    8     ! 13469 146   3469  ! 2     347   3469  !
   +-------------------+-------------------+-------------------+
169 candidates.

[P.O.]

Code: Select all

after singles and intersections:

 245  ea×(25)+4±8 9      14     1457   47     6     b2+34   a134+8           
 47     6         147    2      3      8      149    5       149             
 3     a245+8     1245   1469   1456   469    148    24      7               
 9      1         245    34     8      2347   3457   6       234             
 2468   3         246    5      467    1      478    9       248             
 24568  7         2456   346    9      2346   3458   1       2348           
 1     e2-4       23467  8      46     3469   349   c3(47)   5               
d*46    9        d3*46   7      2      5     d13-4   8      d13-46           
 4567  e-45       8      13469  146    3469   2     c3(47)   3469         

        / n8r1c9
r1c2{n8          } - r1n3{c9 c8} - c8{r7r9}{n4n7} - r8n4{c7c9 c1c3} - c2n4{r7r9 r1} => r1c2 <> 2,5
        \ n8r3c2

h24+5   2458   9      14    a14×5±7 a4+7    6       234    1348           
 47     6      147    2      3       8      149     5      149             
 3      2458   1245   1469   1456    469    148     24     7               
 9      1      245    34     8      b234-7 b345+7   6      234             
 2468   3      246    5      467     1      478     9      248             
 24568  7      2456   346    9       2346  c34+58   1      2348           
 1      24     23467  8      46      3469  d*349   e3(47)  5               
f*46    9     f3*46   7      2       5    fd1*3-4   8     f13-46           
h4-567 g4+5    8      13469  146     3469   2      e3(47)  3469           

r1n7{c5 c6} - r4n7{c6 c7} - c7n5{r4 r6} - c7n3{r6 r7r8} - c8{r7r9}{n4n7} - r8n4{c7c9 c1c3} -
r9c2{n4 n5} - c1n5{r9 r1} => r1c5 <> 5
ste.


[DEFISE]

W-rating = 4
After singles and Box/lines (whip[1]) :

whip[4]: r1n5{c1 c5}- r1n7{c5 c6}- r4n7{c6 c7}- r4n5{c7 .} => -5r3c3
Box/Line: 5c3b4 => -5r6c1
S2-whip[4]: r3c8{n2 n4}- r2n4{c7 NP:19c79}- c3n1{r2 .} => -2r3c3
Naked triplets: 147b1p469 => -4r1c1 -4r1c2 -4r3c2
singles and Box/lines to the end.

[pjb]

Code: Select all

 25-4   *2458    9      | 14     1457   47     | 6     *234    138-4   
*47      6      *147    | 2      3      8      |*149    5      *149   
 3      *2458    125-4  | 1469   1456   469    | 18-4  *24     7     
------------------------+----------------------+---------------------
 9       1       245    | 34     8      2347   | 3457   6      234   
 2468    3       246    | 5      467    1      | 478    9      248   
 24568   7       2456   | 346    9      2346   | 3458   1      2348   
------------------------+----------------------+---------------------
 1      *24      2367-4 | 8      46     3469   | 39-4  *347    5     
*46      9      *346    | 7      2      5      |*134    8     *1346   
 567-4   *45      8      | 13469  146    3469   | 2     *347    369-4   


There's a nice grouped continuous loop of 4's as above:(4)r2c13 = r2c79 - r13c8 = r79c8 - r8c79 = r8c13 - r79c2 = r13c2 - r2c13: loop =>
-4 r1c19, -4 r3c37, -4 r7c37, -4 r9c19. There's a franken jellyfish of 4s (r28b4b6\c1379), with same eliminations.

Then a simple chain: (5)r3c5 = (5-7)r1c5 = (7)r1c6 - (7)r4c6 = (7-5)r4c7 = (5)r4c3 => -5 r3c3,
and ALS: (1=2)r3c3 - (2=1)r2c79, r3c8 => -1 r2c3; btte

Phil

[denis_berthier]

.
Hi François
Excellent solution.
I tried to reproduce it, first using my "reconstruct-path" function (giving it your 3 eliminations: n5r3c3, n2r3c3 and n4r1c1), and I got something similar, but with a g-whip[4], instead of the S2-whip[4]:
biv-chain[4]: r4n5{c3 c7} - b6n7{r4c7 r5c7} - c5n7{r5 r1} - b2n5{r1c5 r3c5} ==> r3c3≠5
whip[1]: c3n5{r6 .} ==> r6c1≠5
g-whip[4]: c3n1{r3 r2} - r2n7{c3 c1} - r2n4{c1 c789} - r3c8{n4 .} ==> r3c3≠2
naked-triplets-in-a-block: b1{r2c1 r2c3 r3c3}{n4 n7 n1} ==> r1c1≠4, r3c2≠4, r1c2≠4
w1-tte


However, when I tried to get something similar directly with my version of the "fewer-steps" algorithm, not only didn't I get this solution, but I found it was impossible to get it that way in gW4:

- the first step, with score 4, can only be:
biv-chain[3]: r8c1{n6 n4} - r2c1{n4 n7} - b7n7{r9c1 r7c3} ==> r7c3≠6
whip[1]: r7n6{c6 .} ==> r9c4≠6, r9c5≠6, r9c6≠6

- the second step, with score 3, can only be:
biv-chain[4]: r8c1{n6 n4} - r2c1{n4 n7} - b7n7{r9c1 r7c3} - b7n3{r7c3 r8c3} ==> r8c3≠6
whip[1]: b7n6{r9c1 .} ==> r5c1≠6, r6c1≠6

- the third step, with score 5, can only be:
g-whip[4]: r8c3{n3 n4} - c2n4{r9 r123} - r2c1{n4 n7} - b7n7{r9c1 .} ==> r7c3≠3
hidden-single-in-a-block ==> r8c3=3
OR
whip[4]: c3n3{r8 r7} - c3n7{r7 r2} - r2c1{n7 n4} - b4n4{r5c1 .} ==> r8c3≠4
naked-single ==> r8c3=3
In both cases, the same RS is reached. Which amounts to saying the 3rd step has essentially only one possibility also.

- the fourth step, with score 2, can only be:
biv-chain[4]: r4n5{c3 c7} - b6n7{r4c7 r5c7} - c5n7{r5 r1} - b2n5{r1c5 r3c5} ==> r3c3≠5
whip[1]: c3n5{r6 .} ==> r6c1≠5

After this point, there are several possibilities, but in any case, no 3-step solution can be reached.

So, this is an interesting case where the differences in our algorithms allow different results:
- did you use the possibility in yours to do 2 steps at a time?
- did you try it in gW4 instead of S2W4?
.

[denis_berthier]

Code: Select all

 25-4   *2458    9      | 14     1457   47     | 6     *234    138-4   
*47      6      *147    | 2      3      8      |*149    5      *149   
 3      *2458    125-4  | 1469   1456   469    | 18-4  *24     7     
------------------------+----------------------+---------------------
 9       1       245    | 34     8      2347   | 3457   6      234   
 2468    3       246    | 5      467    1      | 478    9      248   
 24568   7       2456   | 346    9      2346   | 3458   1      2348   
------------------------+----------------------+---------------------
 1      *24      2367-4 | 8      46     3469   | 39-4  *347    5     
*46      9      *346    | 7      2      5      |*134    8     *1346   
 567-4   *45      8      | 13469  146    3469   | 2     *347    369-4   


There's a nice grouped continuous loop of 4's as above:(4)r2c13 = r2c79 - r13c8 = r79c8 - r8c79 = r8c13 - r79c2 = r13c2 - r2c13: loop =>
-4 r1c19, -4 r3c37, -4 r7c37, -4 r9c19. There's a franken jellyfish of 4s (r28b4b6\c1379), with same eliminations.

We cross posted.
You mean franken jellyfish of 4s (r28b4b9\c1379)?

[DEFISE]

.
- the first step, with score 4, can only be:
biv-chain[3]: r8c1{n6 n4} - r2c1{n4 n7} - b7n7{r9c1 r7c3} ==> r7c3≠6
whip[1]: r7n6{c6 .} ==> r9c4≠6, r9c5≠6, r9c6≠6

Not for me because I randomly choose a candidate whose score is > 1 and is between the best score and the best score – N (where N is a parameter). I added this possibility several months ago.
Here it allows me to also choose 5r3c3 whose score is only 2, instead of 6r7c3.

.
So, this is an interesting case where the differences in our algorithms allow different results:
- did you use the possibility in yours to do 2 steps at a time?

Yes my “Few-Steps V2” algorithm looks for the pair of targets that has the best score. This version V2 directly gives the solution with one try.
But my “Few-Steps V1” algorithm gives me the same result in 3 tries.

.
- did you try it in gW4 instead of S2W4?
.

Yes the 2 versions V1 and V2 work well in g-w and in S2-W.
In fact, I started by looking for a path in W and I had to come to a maximum length of 7 to obtain a solution with less than 5 steps:

whip[4]: r1n5{c1 c5}- r1n7{c5 c6}- r4n7{c6 c7}- r4n5{c7 .} => -5r3c3
Box/Line: 5c3b4 => -5r6c1
whip[7]: r3c8{n2 n4}- c8n2{r3 r1}- r1n3{c8 c9}- r1n8{c9 c2}- r3c2{n8 n5}- r1c1{n5 n4}- r2n4{c1 .} => -2r3c3
Naked triplets: 147b1p469 => -4r1c1 -4r1c2 -4r3c2

Then I tried to eliminate the 2r3c3 in S2-W, without thinking of g-W.

[Mauriès Robert]

Hi all,
One-step solution like this (see puzzle):

P'(4r13c8) : (-4r13c8) => [ 2r3c8 and 4r79c8->4r8c13->48r13c2->25B1p19 ]->5r3c3->5r1c5->7r1c6->7r4c7->5r6c7 => 5B4 empty,
so -4r13c8 impossible => -4B3p3467 and end of puzzle by basic techniques.

puzzle: Show

Robert

[DEFISE]

P'(4r13c8) : (-4r13c8) => [ 2r3c8 and 4r79c8->4r8c13->48r13c2->25B1p19 ]->5r3c3->5r1c5->7r1c6->7r4c7->5r6c7 => 5B4 empty,
so -4r13c8 impossible => -4B3p3467 and end of puzzle by basic techniques.

Hi Robert,
It's a nice application of an anti-track from a set of candidates.
You also have this one, shorter, which eliminates the 2 candidates that I eliminated separately (by whips) in my path above:

P’(14r3c3) : -14r3c3 => 1r2c3 => 49b3p46 => 2r3c8 => 5r3c3 => 5r1c5 => 7r1c6 => 7r4c7 => 5r4 empty

=> -25r3c3 and basics to the end.

[Mauriès Robert]

Hi Robert,
It's a nice application of an anti-track from a set of candidates.
You also have this one, shorter, which eliminates the 2 candidates that I eliminated separately (by whips) in my path above:

P’(14r3c3) : -14r3c3 => 1r2c3 => 49b3p46 => 2r3c8 => 5r3c3 => 5r1c5 => 7r1c6 => 7r4c7 => 5r4 empty

=> -25r3c3 and basics to the end.

Yes François, I had seen this solution, but finding it too close to yours, although formulated differently, I looked for another one.
Robert

[denis_berthier]

.
If you're looking for 1-step solutions at any cost (unrestricted chain lengths), here is one using Forcing-T&E (i.e. conjugated tracks in their naked definition as sets):

FORCING-T&E(S) applied to bivalue candidates n3r1c8 and n3r1c9 :
===> 21 values decided in both cases: n5r9c2 n5r4c7 n7r5c7 n7r4c6 n4r1c6 n1r1c4 n1r9c5 n7r7c8 n6r5c3 n6r8c1 n7r9c1 n4r2c1 n9r7c7 n1r2c7 n6r9c9 n1r8c9 n9r2c9 n7r2c3 n2r4c9 n3r4c4 n7r1c5
stte

[pjb]

denis_berthier wrote

You mean franken jellyfish of 4s (r28b4b9\c1379)?

No, I'll stick by this fish being r28b4b6\c1379. Below from UFG:

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 *  *  . |  .  .  . |  .  *  *       
 *  *  . |  .  .  . |  .  *  *       
 X  X  / |  /  /  / |  /  X  X       
---------+----------+----------     
 X  X  / |  .  .  . |  /  X  X       
 X  X  / |  .  .  . |  /  X  X       
 X  X  / |  .  .  . |  /  X  X       
---------+----------+----------     
 X  X  / |  /  /  / |  /  X  X       
 *  *  . |  .  .  . |  .  *  *       
 *  *  . |  .  .  . |  .  *  *       
 Fig 4E1: rrbb\cccc     

Phil

[denis_berthier]

Hi Phil,
OK, thanks. I didn't look at it the right way.