Contrary "17" Puzzles

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

Postby ronk » Sun Mar 30, 2008 10:51 pm

daj95376 wrote:
Code: Select all
[r4c5]=2 [r1c579]=689      [r1c123]<>689
[r4c5]=8 [r2c5]=9 [r2c2]=8 [r1c123]<> 8

hobiwan wrote: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


Or an ALS chain with endpoint overlap, i.e., if r23c2<>89 then r2c2=8.
Code: Select all
 479   279   49    | 5     2689  1     | 68    3     689
 6   DA89    1     | 37   C89    37    | 4     5     2
 3    A289   5     | 4     69   B28    | 7     689   1
-------------------+-------------------+------------------
 5     4     7     | 69    28    28    | 69    1     3
 2     3     69    | 1     7     4     | 5     68    689
 1     69    8     | 69    3     5     | 2     4     7
-------------------+-------------------+------------------
 4789  679   469   | 2     1     79    | 3     789   5
 79    5     23    | 8     4     3679  | 1     2679  69
 789   1     23    | 37    5     69    | 689   26789 4

            A                            B        C        D
r1c123 -8- ALS:(r23c2 =89|2= r3c2) -2- r3c6 -8- r2c5 -9- r2c2 -8- r1c123 ==> r1c123<>8

daj95376 wrote: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.

The term seems appropriate ... and I believe Mike would do the same for your example.
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Postby daj95376 » Sun Mar 30, 2008 11:08 pm

hobiwan wrote:
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?

mea culpa: Two sectors exchanged in base set. Not so noteworthy after all.

Code: Select all
8..5...6.1...2....5...3...4.8......5...68..4...3..4.7...1...3.8.......9...4..7.16 #EC-2

 *-----------------------------------------------------------*
 | 8     3     279   | 5     4     19    | 1279  6     129   |
 | 1     4     679   | 79    2     68    | 579   358   39    |
 | 5     29    2679  | 179   3     68    | 1279  28    4     |
 |-------------------+-------------------+-------------------|
 | 4     8     29    | 1239  7     1239  | 6     23    5     |
 | 7     12    5     | 6     8     239   | 129   4     1239  |
 | 26    169   3     | 29    5     4     | 8     7     129   |
 |-------------------+-------------------+-------------------|
 | 9     7     1     | 4     6     25    | 3     25    8     |
 | 26    56    8     | 23    1     235   | 4     9     7     |
 | 3     25    4     | 8     9     7     | 25    1     6     |
 *-----------------------------------------------------------*

Code: Select all
 finned Franken Jellyfish c8b8+c3b7|c1b1\r3478   <> 2  [r3c2],[r4c3]
 +-----------------------------------+
 |  .  .  2  |  .  .  .  |  2  .  2  |
 |  .  .  .  |  .  2  .  |  .  .  .  |
 |  .  2  2  |  .  .  .  |  2  2  .  |
 |-----------+-----------+-----------|
 |  .  .  2  |  2  .  2  |  .  2  .  |
 |  .  2  .  |  .  .  2  |  2  .  2  |
 |  2  .  .  |  2  .  .  |  .  .  2  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  2  |  .  2  .  |
 |  2  .  .  |  2  .  2  |  .  .  .  |
 |  .  2  .  |  .  .  .  |  2  .  .  |
 +-----------------------------------+
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Postby daj95376 » Wed Apr 02, 2008 12:16 am

This 17 isn't difficult if you find an elimination on candidate 4. What does it take without eliminating candidate 4???

Code: Select all
.1.7.........5.4..........34..3.....2.....5.....1...8.5...2.6...3.....7......4... #15709

# note: Simple Sudoku takes forever to verify a single solution
# note: after SSTS, finned Swordfish present but not useful
 +-----------------------------------------------------------------------------------------+
 |  3689     1        2345689  |  7        34689    3689     |  289      2569     25689    |
 |  36789    26789    236789   |  2689     5        13689    |  4        1269     126789   |
 |  6789     2456789  256789   |  24689    1689     1689     |  12789    12569    3        |
 |-----------------------------+-----------------------------+-----------------------------|
 |  4        56789    156789   |  3        6789     25       |  1279     1269     12679    |
 |  2        6789     136789   |  4689     6789     6789     |  5        13469    1679     |
 |  3679     5679     35679    |  1        4679     25       |  2379     8        24679    |
 |-----------------------------+-----------------------------+-----------------------------|
 |  5        4789     789      |  89       2        37       |  6        1349     189      |
 |  689      3        24689    |  5689     1689     1689     |  289      7        24589    |
 |  1        26789    26789    |  5689     37       4        |  2389     2359     2589     |
 +-----------------------------------------------------------------------------------------+
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Postby eleven » Wed Apr 02, 2008 12:37 pm

Code: Select all
 +-----------------------------------------------------------------------------------------+
 |  3689     1       #2345689  |  7       @34689    3689     |  289      2569     25689    |
 |  36789    26789    236789   |  2689     5        13689    |  4        1269     126789   |
 |  6789    @2456789  256789   | #24689    1689     1689     |  12789    12569    3        |
 |-----------------------------+-----------------------------+-----------------------------|
 |  4        56789    156789   |  3        6789     25       |  1279     1269     12679    |
 |  2        6789     136789   | @4689     6789     6789     |  5       #13469    1679     |
 |  3679     5679     35679    |  1       #4679     25       |  2379     8       @24679    |
 |-----------------------------+-----------------------------+-----------------------------|
 |  5       #4789     789      |  89       2        37       |  6       @1349     189      |
 |  689      3       @24689    |  5689     1689     1689     |  289      7       #24589    |
 |  1        26789    26789    |  5689     37       4        |  2389     2359     2589     |
 +-----------------------------------------------------------------------------------------+
All 4's are connected with strong links, either # or @ must be 4.
r1c5=4 -> r9c5=3
r5c8=4 -> r6c7=3
i.e. 3 can be eliminated from r9c7
Last edited by eleven on Wed Apr 02, 2008 8:54 am, edited 1 time in total.
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Postby ronk » Wed Apr 02, 2008 12:48 pm

daj95376 wrote:What does it take without eliminating candidate 4???

A large ALS gets you most of the way there. Tersely ...

r7c8 =4= r5c8 -4- ALS:r5c24569 -1- r7c9 =1= r7c8 ==> r7c8=14

Verbosely ...

r7c8 =4= r5c8 -4- ALS:(r5c24569 =4|6789|1= r5c9) -1- r7c9 =1= r7c8 ==> r7c8=14

The latter breaks out key cell r5c9, and lists all cells and all candidates of the ALS. There is a smaller complementary AHS, of course, but I've never liked the notation for an AHS.

[edits 1&2: r5c8 was incorrectly included in the ALS]
[edit 3: added the following]

As noted later by eleven, this is a continuous loop ... with additional eliminations.
Code: Select all
#15709 of Gordon Royle's list of 17s
.1.7.........5.4..........34..3.....2.....5.....1...8.5...2.6...3.....7......4...

After SSTS:
 3689   1       2345689 | 7      4689   3689  | 289    2569    25689
 36789  26789   236789  | 2689   5      13689 | 4      1269    26789-1
 6789   2456789 2456789 | 24689  14689  1689  | 12789  12569   3
------------------------+---------------------+-----------------------
 4      56789   156789  | 3      6789   25    | 1279   1269    2679-1
 2     B6789    13-6789 |B4689  B46789 B6789  | 5     A134-69 B14679
 3679   5679    35679   | 1      4679   25    | 2379   8       24679
------------------------+---------------------+-----------------------
 5      4789    4789    | 89     2      37    | 6      14-39  C1489
 689    3       24689   | 5689   1689   1689  | 289    7       24589
 1      26789   26789   | 5689   37     4     | 2389   2359    2589

           A                         B                 C
r7c8 =4= r5c8 -4- ALS:(r5c24569 =4|6789|1= r5c9) -1- r7c9 =1= r7c8 =4= continuous loop
 ==> r5c3<>6789, r5c8<>69, r24c9<>1 and r7c8=14

All potential eliminations can be read directly from the nice loop notation ... without reference to the pencilmarks.

r7c8 =4= r5c8 -4- ALS:(r5c24569 =4|6789|1= r5c9) -1- r7c9 =1= r7c8 =4= continuous loop
==> r5c3<>6789, r5c8<>69, r24c9<>1 and r7c8=14

Due to the continuous nature of the loop, the ALS becomes locked .... and all weak links become conjugate links.

=4|6789|1= -- Ultimately the ALS contains either 46789 or 67891, i.e., 6789 is unconditionally locked into the set. (This is the reason for the "=4|6789|1=" strong inference notation above.) Other than the cells of the ALS, digits 6789 may be eliminated from all cells of r5. Potentially r5c1378<>6789, but actually r5c3<>6789 and r5c8<>69.

r5c9 -1- r7c9 -- Ultimately, either r5c9=1 or r7c9=1. Potentially r1234689c1<>1, but actually r24c9<>1.

=1= r7c8 =4= -- There is an implied weak link in r7c8. Ultimately either r7c8=1 or r7c8=4. Without looking at the pencilmarks, we know only that r7c8=14. That's the reason I write r7c8=14, not r7c8<>39.

r5c8 -4- ALS:r5c24569 -- Ultimately either r5c8=4 or one of the ALS cells r5c24569=4. Potentially r5c137<>4, but none of these cells contain digit 4.
Last edited by ronk on Thu Apr 03, 2008 9:11 am, edited 3 times in total.
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Postby eleven » Wed Apr 02, 2008 4:17 pm

Dont understand, a ALS with 7 numbers in 5 cells ?
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Postby ronk » Wed Apr 02, 2008 4:24 pm

eleven wrote:Dont understand, a ALS with 7 numbers in 5 cells ?

Maybe not obvious, but there are six cells.
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Postby eleven » Wed Apr 02, 2008 5:14 pm

Still dont get it. Do you mean that r7c8=3 implies r5c9=1 and vice versa ? I cannot see that from the cells you have listed (r7c8 and row 5).
Maybe you can provide a link, which is not too time consuming, to understand the notation.
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Postby daj95376 » Wed Apr 02, 2008 5:16 pm

The (easy) implication chain that I originally found uses candidates 3 & 4 as well. Unfortunately, it's based on an elimination for candidate 4. Of course, I'm an amateur and get to cheat!:D

Code: Select all
[r5c4]=4 [r7c8]=4 [r7c6]=3 [r1c5]=3 [r6c5]=4 => [r5c4]<>4
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Postby ronk » Wed Apr 02, 2008 7:31 pm

eleven wrote:Still dont get it. Do you mean that r7c8=3 implies r5c9=1 and vice versa ? I cannot see that from the cells you have listed (r7c8 and row 5).

Sorry, I incorrectly translated from an AHS to an ALS; original post corrected.

Maybe you can provide a link, which is not too time consuming, to understand the notation.

While I've been using that notation for some time, I don't think it's formally defined anywhere. However, now that the ALS is corrected, it'll probably make sense to you.
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Postby eleven » Wed Apr 02, 2008 7:46 pm

Ah, yes, with the strong link for 4 i can see it. Would write it as
Either r7c8=4 or r5c8=4 -> r5c3=3 -> r5c9=1 -> r7c8=1, i.e. r7c8<>39

Edit: btw the second one gives a loop (with r7c8=1 -> r5c8=4), which also would allow to eliminate 6789 from r5c3 (r5c9<>1 -> r5c38=13) [corrected mistake]
Last edited by eleven on Thu Apr 03, 2008 4:02 am, edited 1 time in total.
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Postby daj95376 » Thu Apr 03, 2008 12:54 am

I settled on an implication chain that results in a contradiction. Maybe you'll have better luck.

Code: Select all
.9......25..3........6.....3.6...4......81...7.........8..9......2....3.......67. #24299

 +-----------------------------------------------------------------------------------------+
 |  1468     9        1347     |  1578     1457     4578     |  13578    14568    2        |
 |  5        2467     147      |  3        1247     24789    |  1789     14689    146789   |
 |  1248     2347     1347     |  6        12457    245789   |  135789   14589    1345789  |
 |-----------------------------+-----------------------------+-----------------------------|
 |  3        125      6        |  2579     257      257      |  4        12589    15789    |
 |  249      245      459      |  2457     8        1        |  2357     256      3567     |
 |  7        1245     8        |  2459     36       36       |  1259     1259     159      |
 |-----------------------------+-----------------------------+-----------------------------|
 |  146      8        13457    |  157      9        34567    |  125      1245     145      |
 |  1469     4567     2        |  1578     14567    45678    |  1589     3        14589    |
 |  149      345      13459    |  1258     12345    23458    |  6        7        14589    |
 +-----------------------------------------------------------------------------------------+

Code: Select all
[r6c6]=3 [r7c3]=3 [r3c2]=3 [r5c9]=3 [r5c8]=6 [r1c1]=6 => [r8c2b7]=67 contradiction!
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Postby Draco » Thu Apr 03, 2008 2:40 am

daj95376 wrote:I settled on an implication chain that results in a contradiction. Maybe you'll have better luck.

Code: Select all
.9......25..3........6.....3.6...4......81...7.........8..9......2....3.......67.
#24299



I started a chain in the same spot, but came up with an ALS triplet (or is this considered a Forcing Net?):

r6c6-3-r7c6=3=r7c3=7=r8c2 and
r6c6=3=r6c5=6=r8c5 and
rc6c6-6-r7c6=6=r7c1-6-r1c1=6=r2c2, ergo
r2c2<>7, r8c2<>6, r8c5<>7

SSTS
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Postby daj95376 » Thu Apr 03, 2008 5:59 am

Draco, if you take your first chain and extend your third chain, then I believe you have a forcing chain from [r6c6] => [r8c2]<>6, and this is sufficient to crack the puzzle so that SSTS can complete the solution.
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Postby Draco » Thu Apr 03, 2008 6:07 am

daj95376 wrote:Draco, if you take your first chain and extend your third chain, then I believe you have a forcing chain from [r6c6] => [r8c2]<>6, and this is sufficient to crack the puzzle so that SSTS can complete the solution.


Whoa -- Daj. Very nicely done!
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