## Contrary "17" Puzzles

Everything about Sudoku that doesn't fit in one of the other sections
daj95376 wrote:
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`[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:
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`[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.
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` 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        Dr1c123 -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.
ronk
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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.

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`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     | *-----------------------------------------------------------*`

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` 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  .  .  | +-----------------------------------+`
daj95376
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This 17 isn't difficult if you find an elimination on candidate 4. What does it take without eliminating candidate 4???

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`.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     | +-----------------------------------------------------------------------------------------+`
daj95376
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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.
eleven

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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]

As noted later by eleven, this is a continuous loop ... with additional eliminations.
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`#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                 Cr7c8 =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.
ronk
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Dont understand, a ALS with 7 numbers in 5 cells ?
eleven

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

Maybe not obvious, but there are six cells.
ronk
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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.
eleven

Posts: 1798
Joined: 10 February 2008

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!

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`[r5c4]=4 [r7c8]=4 [r7c6]=3 [r1c5]=3 [r6c5]=4 => [r5c4]<>4`
daj95376
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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.
ronk
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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.
eleven

Posts: 1798
Joined: 10 February 2008

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

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`.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!`
daj95376
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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
Draco

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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.
daj95376
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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!
Draco

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