The New Sudoku Players' Forum

[SteveG48]

Code: Select all

 *-----------*
 |..8|...|2..|
 |.93|..4|.5.|
 |24.|...|73.|
 |---+---+---|
 |...|15.|..2|
 |...|2.8|...|
 |8..|.47|...|
 |---+---+---|
 |.29|...|.15|
 |.6.|5..|48.|
 |..7|...|3..|
 *-----------*


[jco]

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.-----------------------------------------.
| 167  17   8  | 367 b37  5  | 2   9   4  |
| 67   9    3  |c678* 2   4  | 1   5   68*|
| 2    4    5  |d689* 18 e19 | 7   3   68*|
|--------------+-------------+------------|
| 79   3    46 | 1    5   9-6| 8   47  2  |
| 179  157  46 | 2   a36  8  | 59  47  13 |
| 8    15   2  | 39   4   7  | 59  6   13 |
|--------------+-------------+------------|
| 4    2    9  | 78   78  3  | 6   1   5  |
| 3    6    1  | 5    9   2  | 4   8   7  |
| 5    8    7  | 4    16 f16 | 3   2   9  |
'-----------------------------------------'

UR(68)r23 c49 using internals
(6=3)r5c5 - (3=7)r1c5 - (7)r2c4 = UR = (9)r3c4 - (9=1)r3c6 - (1=6)r9c6 => -6 r4c6; ste

[shye]

using the same UR as jco, but differently ღ ' ⌣ ' ღ

Code: Select all

.--------------.-------------.------------.
| 167  17   8  | 367 #37  5  | 2   9   4  |
| 67   9    3  |*678  2   4  | 1   5  *68 |
| 2    4    5  |*689  18  19 | 7   3  *68 |
:--------------+-------------+------------:
| 79   3    46 | 1    5   69 | 8   47  2  |
| 179  157  46 | 2    6-3 8  | 59  47  13 |
| 8    15   2  |#39   4   7  | 59  6   13 |
:--------------+-------------+------------:
| 4    2    9  | 78   78  3  | 6   1   5  |
| 3    6    1  | 5    9   2  | 4   8   7  |
| 5    8    7  | 4    16  16 | 3   2   9  |
'--------------'-------------'------------'

UR y-wing
68UR in r23c49, guardians (79)r23c4
(3=7)r1c5 - (7=9)r23c4 - (9=3)r6c4
=> -3r5c5 stte

always excited when i find one of these nice puzzle!

[jco]

(...)
UR y-wing
68UR in r23c49, guardians (79)r23c4
(3=7)r1c5 - (7=9)r23c4 - (9=3)r6c4
=> -3r5c5 stte

always excited when i find one of these nice puzzle!

Very nice! and nice puzzle indeed!

[P.O.]

Code: Select all

after singles:

b+167   157   8   dc3+*67  c13*67  c15*6   2     9     4             
 67     9     3     -678    2       4      1     5     68             
 2      4     56    -689    1-68    15-69  7     3     68             
 679    3     46    1       5       69     8     47    2             
a-1679  157   456   2       36      8      59    47    ×13             
 8      ×15   2    e+39     4       7      59    6    f+1-3             
 4      2     9     78      78      3      6     1     5             
 3      6     1     5       9       2      4     8     7             
 5      8     7     4       16      16     3     2     9             

depth: 4  candidate: 1  from cells
(((5 9 6) (1 3)) ((6 2 4) (1 5)))

((1 0) (5 1 4) (1 6 7 9))
((1 0) (1 1 1) (1 6 7))
((6 1 1 11) ((1 4 2) (3 6 7)) ((1 5 2) (1 3 6 7)) ((1 6 2) (1 5 6)))
((6 2 18) (1 4 2) (3 6 7))
((3 3 10) (6 4 5) (3 9))
((1 4 9) (6 9 6) (1 3))

ste.


[Leren]

Code: Select all

*-------------------------------------*
| 167  17   8  | 367 37 5  | 2  9  4  |
| 67   9    3  | 678 2  4  | 1  5  68 |
| 2    4    5  | 689 18 19 | 7  3  68 |
|--------------+-----------+----------|
|a79   3    46 | 1   5  69 | 8  47 2  |
|b179 d15-7 46 | 2   36 8  |c59 47 13 |
| 8    15   2  | 39  4  7  | 59 6  13 |
|--------------+-----------+----------|
| 4    2    9  | 78  78 3  | 6  1  5  |
| 3    6    1  | 5   9  2  | 4  8  7  |
| 5    8    7  | 4   16 16 | 3  2  9  |
*-------------------------------------*

(7=9) r4c1 - r5c1 = (9-5) r5c7 = (5) r5c2 => - 7 r5c2; stte

Leren

[RSW]

Code: Select all

 +------------+--------------+------------+
 | 167 17  8  |  367 c37  5  | 2  9   4   |
 | 67  9   3  |d#678  2   4  | 1  5  #68  |
 | 2   4   5  |d#689  18  19 | 7  3  #68  |
 +------------+--------------+------------+
 | 79  3   46 |  1    5   69 | 8  47  2   |
 | 179 157 46 |  2  b*6-3 8  | 59 47 a13  |
 | 8   15  2  | e39   4   7  | 59 6  *1-3 |
 +------------+--------------+------------+
 | 4   2   9  |  78   78  3  | 6  1   5   |
 | 3   6   1  |  5    9   2  | 4  8   7   |
 | 5   8   7  |  4    16  16 | 3  2   9   |
 +------------+--------------+------------+


More testing with the new mixed chain routine in my solver, it also came up with a UR move:
UR(68)r23c49
(3)r5c9=(3)r5c5 - (3=7)r1c5 - (7)r2c4=UR=(9)r3c4 - (9=3)r6c4 => -3r5c5, -3r6c9; stte

I was surprised to see that one of the eliminations was -3r5c5 which is the second link in the chain. When building a chain manually, it would never occur to me to include a link that would also be an elimination cell (unless it's at the end), but I can't see any flaw in the logic. (Essentially, it's the same chain as shye's with two additional links to get an additional elimination. I guess it makes more sense looking at it from right to left.)

[marek stefanik]

Interesting example, it seems it could happen when solving manually, too, but I don't think it has happened to me yet.
Anyway, such a chain can never provide more value than its shorter version, since the additional links get resolved with singles (or other techniques you would include in the chain).
Here after eliminating 3r5c5, you get the single 3r5c9, which eliminates 3r6c9.
Therefore you can just check for these cases and shorten the chain if they occur.

Marek

[RSW]

Anyway, such a chain can never provide more value than its shorter version, since the additional links get resolved with singles (or other techniques you would include in the chain).

The extra links were the result of a modification that I made to the chain finder code in order to resolve a problem. Previously, it would terminate as soon as it found an elimination. However, it appeared to miss some longer chains that could have given different eliminations. I revised the code so that it would continue to extend the chain, even if an elimination had already been found. It would then save both the shorter and longer chains. After all chains have been found (often hundreds of thousands of them due to the many permutations), the routine then deletes chains that duplicate the eliminations of shorter chains. In this case there was indeed a short chain that gave the same elimination as the short UR chain. Since the short UR chain was slightly longer than the non-UR chain, the short UR chain was deleted, leaving only the short non-UR chain. The longer UR chain was not deleted because it had a second elimination, and that is the chain that I posted.

The chain finder, as it exists, uses a standard recursive branching technique, and is not very efficient due to the thousands of redundant chains that it finds. Though inefficient, it has served its purpose in testing the other parts of the chain building code. I'm now rewriting a non-recursive version of the chain finder, which should be much more efficient.

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------+-------------+-------------+
   ! 167 17  8   ! 367 37  5   ! 2   9   4   !
   ! 67  9   3   ! 678 2   4   ! 1   5   68  !
   ! 2   4   5   ! 689 18  19  ! 7   3   68  !
   +-------------+-------------+-------------+
   ! 79  3   46  ! 1   5   69  ! 8   47  2   !
   ! 179 157 46  ! 2   36  8   ! 59  47  13  !
   ! 8   15  2   ! 39  4   7   ! 59  6   13  !
   +-------------+-------------+-------------+
   ! 4   2   9   ! 78  78  3   ! 6   1   5   !
   ! 3   6   1   ! 5   9   2   ! 4   8   7   !
   ! 5   8   7   ! 4   16  16  ! 3   2   9   !
   +-------------+-------------+-------------+

===> There are 27 W1-anti-backdoors:
n6r1c1 n1r1c2 n3r1c4 n7r1c5 n7r2c1 n1r3c5 n9r3c6 n9r4c1 n4r4c3 n6r4c6 n7r4c8 n1r5c1 n5r5c2 n7r5c2 n6r5c3 n3r5c5 n9r5c7 n4r5c8 n1r5c9 n1r6c2 n9r6c4 n5r6c7 n3r6c9 n7r7c4 n8r7c5 n6r9c5 n1r9c6
all of which give rise to a 1-step solution with whips[≤6]

The simplest two require only bivalue-chains[3]:

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biv-chain[3]: r6c2{n1 n5} - b6n5{r6c7 r5c7} - r5n9{c7 c1} ==> r5c1≠1
stte

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biv-chain[3]: r4c1{n7 n9} - r5n9{c1 c7} - r5n5{c7 c2} ==> r5c2≠7
(same as Leren's chain: (7=9) r4c1 - r5c1 = (9-5) r5c7 = (5) r5c2 => - 7 r5c2)
stte

For those who like 2D-chains, there's also a bivalue-chain[4] in rn-space:

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biv-chain-rn[4]: r1n6{c4 c1} - r1n1{c1 c2} - r6n1{c2 c9} - r6n3{c9 c4} ==> r1c4≠3
stte