Contrary "17" Puzzles

Everything about Sudoku that doesn't fit in one of the other sections

Postby Mike Barker » Sat Mar 22, 2008 5:49 am

StrmCkr, your first ALS has a double restricted common. That means both ALS are locked independently and you get eliminations from candidates which are not restricted common and see one or the other ALS (in this case 379 in box 8). For the restricted common candidates the target must see both ALS:
Code: Select all
A=1 cell ALS xz-mer: r2c4 -28- r89c4|r7c56 => r4c4<>2,r8c6<>379
+-------------------+----------------------+----------------+
| 389    359   359  |     1   389       4  |    2    6   7  |
|  68      1     7  |    28* 2568     258  |    4    3   9  |
| 369      4     2  |   379   369     379  |    8    5   1  |
+-------------------+----------------------+----------------+
|  39  23569  3569  |  39-2     7       1  |  359    8   4  |
|   1    359     4  |     6  3589    3589  | 3579  279  23  |
|   7   2359     8  |     4  2359    2359  |  359    1   6  |
+-------------------+----------------------+----------------+
|   2   3679   369  |     5    39b    379b |    1    4   8  |
|   4    379    39  | 23789b    1  28-379  |    6  279   5  |
|   5      8     1  |   279b    4       6  |  379  279  23  |
+-------------------+----------------------+----------------+

What I really like is this second chain. I keep looking for some clever way to show the elimination as a single chain, but for now I guess I just have to look at it as a deja vu loop. Speaking of deja vu, this pattern (a grouped Turbot fish) was the subject of my first post on this forum - now that's deja vu.
Code: Select all
2-element grouped X-cycle: r4c1 =3= r4c4 -3- r56c6 =3= r3c6 ~3~  => r3c1<>3
2-element grouped X-cycle: r4c1 =9= r4c4 -9- r56c6 =9= r3c6 ~9~  => r3c1<>9
+----------------+-------------------+---------------+
|  389   39   5  |    1   389     4  |   2    6   7  |
|   68    1   7  |   28  2568   258  |   4    3   9  |
| 6-39    4   2  |    7   369    39* |   8    5   1  |
+----------------+-------------------+---------------+
|   39*   2   6  |   39*    7     1  |   5    8   4  |
|    1  359   4  |    6  3589  3589* | 379  279  23  |
|    7  359   8  |    4  2359  2359* |  39    1   6  |
+----------------+-------------------+---------------+
|    2    6  39  |    5    39     7  |   1    4   8  |
|    4    7  39  | 2389     1    28  |   6   29   5  |
|    5    8   1  |   29     4     6  | 379  279  23  |
+----------------+-------------------+---------------+
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Postby StrmCkr » Sat Mar 22, 2008 6:05 am

StrmCkr, your first ALS has a double restricted common. That means both ALS are locked independently and you get eliminations from candidates which are not restricted common and see one or the other ALS (in this case 379 in box 8). For the restricted common candidates the target must see both ALS:
Code: Select all
A=1 cell ALS xz-mer: r2c4 -28- r89c4|r7c56 => r4c4<>2,r8c6<>379
+-------------------+----------------------+----------------+
| 389    359   359  |     1   389       4  |    2    6   7  |
|  68      1     7  |    28* 2568     258  |    4    3   9  |
| 369      4     2  |   379   369     379  |    8    5   1  |
+-------------------+----------------------+----------------+
|  39  23569  3569  |  39-2     7       1  |  359    8   4  |
|   1    359     4  |     6  3589    3589  | 3579  279  23  |
|   7   2359     8  |     4  2359    2359  |  359    1   6  |
+-------------------+----------------------+----------------+
|   2   3679   369  |     5    39b    379b |    1    4   8  |
|   4    379    39  | 23789b    1  28-379  |    6  279   5  |
|   5      8     1  |   279b    4       6  |  379  279  23  |
+-------------------+----------------------+----------------+


doesn't r4c4 see the 2 common candidate from both als?
i didn't realize the other eliminations could also be vaild.
(i got some help with the wording again from scanraid.com solver)
my original move i did does elliminate the 379 from r8C6 but it didnt show up on the listing from the online solver so i didn't include it.

since it didn't list the move as vaild i left it out and worked with what it helpd show.

the grouped fish move after it is nice.

looks like my originial move that i had done after the als but since it didn't list it as a valid move on the solver so i droped it and did a bunch of other stuff instead.

it does save alot of steps this way.

i could write it as a
forcing chain

# are weak links that are removed when any of the *'s are active.

Code: Select all
+----------------+-------------------+---------------+
|  389   39   5  |    1   389#     4  |   2    6   7  |
|   68    1   7  |   28  2568   258  |   4    3   9  |
| 6-39    4   2  |    7   369#    39* |   8    5   1  |
+----------------+-------------------+---------------+
|   39*   2   6  |   39*    7     1  |   5    8   4  |
|    1  359   4  |    6  3589  3589 | 379  279  23  |
|    7  359   8  |    4  3259  2359 |  39    1   6  |
+----------------+-------------------+---------------+
|    2    6  39  |    5    39*     7  |   1    4   8  |
|    4    7  39  | 2389#     1    28  |   6   29   5  |
|    5    8   1  |   29#     4     6  | 379  279  23  |
+----------------+-------------------+---------------+


(how i would write it )

both out comes same choice.

R4c1 (9) > R4c4(3) > R7C5(3) > R3C6(3) > R3C1(6)
R4C1 (3) > R4C4 (9) > R7C5(9) > R3C6(9) > R3C1(6)

(is this correct wording?) {edit:lacks all the linked cells that get elliminated by any of the listed cells being a 3/9 choice}
r4c1=3/9=R4C4=3/9=R7C5=3/9=R3c6 <39> R3c1 therefore R3c1(6)
Last edited by StrmCkr on Sat Mar 22, 2008 4:39 pm, edited 3 times in total.
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Postby eleven » Sat Mar 22, 2008 10:29 am

Mike Barker wrote:
Code: Select all
2-element grouped X-cycle: r4c1 =3= r4c4 -3- r56c6 =3= r3c6 ~3~  => r3c1<>3
2-element grouped X-cycle: r4c1 =9= r4c4 -9- r56c6 =9= r3c6 ~9~  => r3c1<>9
+----------------+-------------------+---------------+
|  389   39   5  |    1   389     4  |   2    6   7  |
|   68    1   7  |   28  2568   258  |   4    3   9  |
| 6-39    4   2  |    7   369    39* |   8    5   1  |
+----------------+-------------------+---------------+
|   39*   2   6  |   39*    7     1  |   5    8   4  |
|    1  359   4  |    6  3589  3589* | 379  279  23  |
|    7  359   8  |    4  2359  2359* |  39    1   6  |
+----------------+-------------------+---------------+
|    2    6  39  |    5    39     7  |   1    4   8  |
|    4    7  39  | 2389     1    28  |   6   29   5  |
|    5    8   1  |   29     4     6  | 379  279  23  |
+----------------+-------------------+---------------+
Note that with this remote naked pair 39 - given by the common (grouped) strong links in row 4 and column 6 to box 5 - you also can eliminate 39 in r56c5 (though its not necessary here to solve the puzzle).
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Postby ronk » Sat Mar 22, 2008 10:48 am

daj95376 wrote:If I knew ALS, I bet this would be even easier!

Code: Select all
[r5c5]=3 => [r7c5]=9 => contradiction in [b2]~379 => [r5c5]<>3
[r5c5]=9 => [r7c5]=3 => contradiction in [b2]~379 => [r5c5]<>9

[r6c5]=3 => [r7c5]=9 => contradiction in [b2]~379 => [r6c5]<>3
[r6c5]=9 => [r7c5]=3 => contradiction in [b2]~379 => [r6c5]<>9

Your deduction can be explained by a doubly-linked ALS xz-rule, aka ALS xz-mer (mutual exclusion rule), aka a Sue de Coq.
Code: Select all
 389    359    359   |  1     B389    4     |  2      6      7
 68     1      7     | B28    B2568  B258   |  4      3      9
 369    4      2     |  379   B369    379   |  8      5      1
---------------------+----------------------+-------------------
 39     23569  3569  |  392    7      1     |  359    8      4
 1      359    4     |  6      58-39  3589  |  3579   279    23
 7      2359   8     |  4      25-39  2359  |  359    1      6
---------------------+----------------------+-------------------
 2      3679   369   |  5     A39     379   |  1      4      8
 4      379    39    |  23789  1      28379 |  6      279    5
 5      8      1     |  279    4      6     |  379    279    23

  A                          B                     A
r7c5 -3- ALS:(r13c5,r2c123 =3|2568|9= r13c5) -9- r7c5 -3- continuous loop implies r56c5<>39

As a Sue de Coq, set B would be split into two sets, AALS r13c5 and ALS r2c456. The AALS shares digits 39 with ALS r7c5, and shares digits 68 with ALS r2c456.
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Postby ronk » Sat Mar 22, 2008 11:10 am

edit: deleted a bogus constraint set POV
Last edited by ronk on Sun Mar 23, 2008 10:05 am, edited 2 times in total.
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Postby hobiwan » Sat Mar 22, 2008 6:33 pm

ronk wrote:An opening move for #40_2:

r2c4 -2- ALS:(r89c4,r7c56 =2|379|8= r89c4) -8- r2c4 -2- continuous loop

... implies r4c4<>2, r8c6<>379


I had the same elimination, but as a Sue de Coq: [r89c4] - {23789} ([r2c4] - {28}, [r7c56] - {379}) => [r4c4]<>2, [r8c6]<>3, [r8c6]<>7, [r8c6]<>9
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Postby daj95376 » Sat Mar 22, 2008 9:44 pm

ronk wrote:A constraint set POV may provide clues for writing single chains in the future.

In this case, digits 3&9 in constraints r4, c6 and r3c1 are covered by constraints r3, c1 and b5. Since digits 3&9 in r3c1 are covered twice, they may be eliminated. [edit: The double cover is required because r3c1 is a member of the base set. Only a single cover is required (by b5) for eliminations r56c5<>39.]

Well, you managed to lose me, but that's not difficult.

Your constraint set has five cells that are in the cover set more often than they are in the base set. However, you only chose to perform eliminations in three of them. Candidates 3&9 can also be eliminated from [r1c1], but things fall apart when eliminating candidates 3&9 in [r3c5].
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Postby ronk » Sun Mar 23, 2008 2:10 pm

daj95376 wrote:things fall apart when eliminating candidates 3&9 in [r3c5].

Oops, I miscounted the set members. My base set has five members while my cover set has six members. This means the equivalent of an unfinned fish does not exist.

Found nothing to salvage, so I deleted the prior post.
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Postby StrmCkr » Sun Mar 23, 2008 8:43 pm

Code: Select all
+----------------+-------------------+---------------+
|  389   39   5  |    1   8-39#     4  |   2    6   7  |
|   68    1   7  |   28  2568   258  |   4    3   9  |
| 6-39X    4   2  |    7   39-6#@    39* |   8    5   1  |
+----------------+-------------------+---------------+
|   39*   2   6  |   39*    7     1  |   5    8   4  |
|    1  359   4  |    6  58-39#  3589 | 379  279  23  |
|    7  359   8  |    4  25-39#  2359 |  39    1   6  |
+----------------+-------------------+---------------+
|    2    6  39  |    5    39*     7  |   1    4   8  |
|    4    7  39  | 2389*#     1    28  |   6   29   5  |
|    5    8   1  |   29#     4     6  | 379  279  23  |
+----------------+-------------------+---------------+

* = stong link
# = weakly linked
x = forced reduction by the strong chain 3/9
@ = a new hidden strong link

found some additional reductions based on my original chain
where 1 weak cover sets becomes a strong link (becoming a hidden pair) indicated by the @ forced by the X.

the affected parts of the chain are the weaklinks that have 2 strong links attached.

from the forced placement of the 6 in R3C1
R3C5+R7C5 form a hidden strong pair of 3/9

in the weak links attached i didn't list befor was
that R1C5 = 8 from either of chains reductions. (also indicated by the hidden pair)

and that from the hidden pair
all weaklinks in line of sight are further reduced by 39
therefor R56C5 cannot = 3,9

R4c1 (9) > R4c4(3) > R7C5(3) > R3C6(3) > R3C1(6) > R3C5(3) > R1C5(8)

R4C1 (3) > R4C4 (9) > R7C5(9) > R3C6(9) > R3C1(6) > R3C5(9) > R1C5(8)
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Postby daj95376 » Sat Mar 29, 2008 6:23 am

After gsf posted his list of hard 17s, I debated whether or not to continue this thread. On the odd chance there's still interest, I'll add this puzzle. I must admit that I'm still debating if it qualifies as contrary.

Code: Select all
Puzzle #40_5:

+-----------------------------------------------------------------------------+
|  4789    2789    489    |  5       2689    1      |  689     3       689    |
|  6       89      1      |  37      89      37     |  4       5       2      |
|  3       289     5      |  4       69      28     |  7       689     1      |
|-------------------------+-------------------------+-------------------------|
|  5       4       7      |  69      28      28     |  69      1       3      |
|  2       3       69     |  1       7       4      |  5       689     689    |
|  1       689     689    |  69      3       5      |  2       4       7      |
|-------------------------+-------------------------+-------------------------|
|  4789    6789    4689   |  2       1       79     |  3       789     5      |
|  79      5       23     |  8       4       3679   |  1       2679    69     |
|  789     1       23     |  37      5       69     |  689     26789   4      |
+-----------------------------------------------------------------------------+
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Postby hobiwan » Sun Mar 30, 2008 4:59 pm

Puzzle #40_5:
I tried to come up with a solution without chains (as a challenge):
Code: Select all
.----------------------.----------------------.-----------------------.
| 4789    2789   489   | 5      A2689   1     | A689    3      A689   |
| 6      B89     1     | 37     C89     37    |  4      5       2     |
| 3       289    5     | 4       69     28    |  7      689     1     |
:----------------------+----------------------+-----------------------:
| 5       4      7     | 69     C28     28    |  69     1       3     |
| 2       3      69    | 1       7      4     |  5      689     689   |
| 1       689    689   | 69      3      5     |  2      4       7     |
:----------------------+----------------------+-----------------------:
| 4789    6789   4689  | 2       1      79    |  3      789     5     |
| 79      5      23    | 8       4      3679  |  1      2679    69    |
| 789     1      23    | 37      5      69    |  689    26789   4     |
'----------------------'----------------------'-----------------------'
Almost Locked Set XY-Wing: A=[r1c579] - {2689}, B=[r2c2] - {89}, C=[r24c5] - {289}, Y,Z=2,9, X=8 => [r1c123]<>8

Locked Candidates Type 1 (Pointing): 8 in b1 => [r67c2]<>8
Hidden Single: [r6c3]=8
Finned Jellyfish: 9 r2346 c2457 f[r3c8] => [r1c7]<>9
Sashimi Jellyfish: 9 r2346 c2458 f[r4c7] => [r5c8]<>9
W-Wing: 6 in [r1c7],[r5c8] connected through 8 in [r15c9] => [r3c8],[r4c7]<>6

Singles

After the Sashimi Jellyfish there is a nice Continous Nice Loop:
Continuous Nice Loop [r1c1]=4=[r7c1]=8=[r7c8]-8-[r5c8]-6-[r5c3]-9-[r1c3]-4-[r1c1] => [r5c9]<>6, [r7c1]<>7, [r39c8]<>8, [r7c13]<>9
the W-Wing is easier though, so I went with it.
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Postby daj95376 » Sun Mar 30, 2008 6:31 pm

Hobiwan, thanks for an interesting solution. I'm amazed at how many ALS eliminations are equivalent to short forcing chains/nets.

Code: Select all
[r4c5]=2 [r1c579]=689      [r1c123]<>689
[r4c5]=8 [r2c5]=9 [r2c2]=8 [r1c123]<> 8


If you check, your finned Jellyfish is actually Sashimi. The only reason I point this out is because you can get both eliminations at once as a ...

Code: Select all
Siamese (Sashimi finned) Jellyfish r2346\c245+c7|c8   <> 9  [r1c7],[r5c8]

where c7|c8 means c7 -or- c8 can alternately be selected for each of the Siamese fish.

I added the Sashimi finned to keep tarek happy.

[ronk: I talked to Mike Barker some time back and he said it was okay for me to use/steal Siamese. Since the fish are of the same size, the term Siamese is appropriate.]
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Postby hobiwan » Sun Mar 30, 2008 7:26 pm

daj95376 wrote:Hobiwan, thanks for an interesting solution. I'm amazed at how many ALS eliminations are equivalent to short forcing chains/nets.

Code: Select all
[r4c5]=2 [r1c579]=689      [r1c123]<>689
[r4c5]=8 [r2c5]=9 [r2c2]=8 [r1c123]<> 8

I confess, that I am still thoroughly confused by the various types of chains and their notation. For me everything boils down to the same thing (at least with simpler types of chains): A digit can only be forced in a cell if it is absent from all other cells in one of the houses. Whether you write that as a forcing chain/net/AIC/ALS with or whithout grouped nodes is not really important (for me at least!).
As to the ALS-XY-Wing I see it more as a general case of XY-Chain:
Code: Select all
[r2c2]<>8 [r24c5]=28 [r1c579]=689 => [r1c123]<>8
[r1c123]<>8 [r1c123]=269 [r24c5]=89 [r2c2]=8 => [r1c123]<>8


daj95376 wrote:If you check, your finned Jellyfish is actually Sashimi. The only reason I point this out is because you can get both eliminations at once as a ...

Code: Select all
Siamese Sashimi Jellyfish r2346\c245+c7|c8   <> 9  [r1c7],[r5c8]

where c7|c8 means c7 -or- c8 can alternately be selected for each of the Siamese fish.

I see it now. After the discussion regarding sashimi on the Ultimate Fish Guide I decided not to bother with sashimi anymore:D (I only check on singles without fins, which is why I missed the first one). But if I find some time I have to implement Siamese Fish into my solver (you posted a solution somewhere a while back with a Siamese Franken Swordfish. My solver missed that and needed another Franken Swordfish later on where you only had to use Locked Candidates).
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Postby daj95376 » Sun Mar 30, 2008 7:54 pm

Hobiwan, as far as I know, all of my Siamese examples have a pair of rows or a pair of columns for the -or- part of the expression. Recently, I ran into a Siamese Franken Swordfish where it appeared boxes could alternate in the -or- part of the expression. It almost knocked me out of my chair:!:
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Postby hobiwan » Sun Mar 30, 2008 9:21 pm

daj95376 wrote:Hobiwan, as far as I know, all of my Siamese examples have a pair of rows or a pair of columns for the -or- part of the expression. Recently, I ran into a Siamese Franken Swordfish where it appeared boxes could alternate in the -or- part of the expression. It almost knocked me out of my chair:!:

Do you have that example somewhere?
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