Contrary "17" Puzzles

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

Postby eleven » Thu Apr 03, 2008 7:46 am

Code: Select all
 +-----------------------------------------------------------------------------------------+
 |  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    |
 +-----------------------------------------------------------------------------------------+
Either r7c1=6 or r7c6=6 -> r7c3=3 -> r8c2=7 -> r2c2=6, i.e. r1c1<>6, r8c2<>6 [corrected typo]
Last edited by eleven on Thu Apr 03, 2008 6:27 am, edited 2 times in total.
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Postby hobiwan » Thu Apr 03, 2008 9:30 am

daj95376 wrote: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     |
 +-----------------------------------------------------------------------------------------+

Discontinuous Nice Loop [r1c3]=4=[r1c5]=3=[r9c5]-3-[r7c6]=3=[r7c8]=4=[r7c2]-4-[r3c2]=4=[r1c3] => [r1c3]<>235689 (or [r1c3]=4)
Does setting 4 instead of eliminating 4 qualify?
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Postby hobiwan » Thu Apr 03, 2008 9:36 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

 +-----------------------------------------------------------------------------------------+
 |  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!

Discontinuous Nice Loop (again): [r2c2]=6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1]-6-[r1c1]=6=[r2c2] => [r2c2]<>247 (or [r2c2]=6)
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Postby eleven » Thu Apr 03, 2008 10:33 am

The "short version" would be enough:
6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1] -> r8c2<>6
Edited mistake, thanks to ronk
Last edited by eleven on Thu Apr 03, 2008 12:51 pm, edited 1 time in total.
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Postby ronk » Thu Apr 03, 2008 1:20 pm

eleven wrote: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]

You are correct about this being a continuous loop. However, I don't believe r5c9<>1 and r5c8<>4 are valid eliminations.

I again edited my original post here, this time to illustrate the continuous loop you noted. I also added a brief explanation of my nice loop notation for the ALS.
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Postby ronk » Thu Apr 03, 2008 2:03 pm

eleven wrote:The "short version" would be enough:
6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1] -> r7c1=6

Your implied complete nice loop is ..

[r7c1]=6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1] -> r7c1=6

... but what of the candidate 6 in r8c1?
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Postby daj95376 » Thu Apr 03, 2008 3:54 pm

eleven wrote:Either r7c1=6 or r7c6=6 -> r7c3=3 -> r8c2=7 -> r2c2=6, i.e. r1c1<>6, r8c2<>6 [corrected typo]

Drop the part in red and you still have enough to crack the puzzle. Or, you could change your short version slightly.

6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1]-6-[r8c2] -> [r8c2]<>6
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Postby eleven » Thu Apr 03, 2008 4:49 pm

ronk wrote:
eleven wrote:The "short version" would be enough:
6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1] -> r7c1=6

... but what of the candidate 6 in r8c1?

Thanks ronk, this was not my day. I found a mistake and typos myself in 2 posts, now you pointed out another mistake. Of course i only can say "-> r8c2<>6", but this also solves the puzzle.
ronk wrote:
eleven wrote: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]

You are correct about this being a continuous loop. However, I don't believe r5c9<>1 and r5c8<>4 are valid eliminations.
I did not mean here, that they can be eliminated, but that the implication r5c9<>1 -> r5c38=13 - together with r5c3=3 in the chain - allows to eliminate 6789 from r5c3 (see below)
I again edited my original post here, this time to illustrate the continuous loop you noted. I also added a brief explanation of my nice loop notation for the ALS.
Thanks for that. I think, i understand it now. It also shows an advantage of the notation. Its easier to see all possible eliminations from the loop.

Here is, how i would have to explain the same eliminations.
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     |
 +-----------------------------------------------------------------------------------------+
The eliminations were: r5c3<>6789, r5c8<>69, r24c9<>1 and r7c8=14

My loop was:
r5c8=4 -> r5c3=3 -> r5c9=1 -> r7c9<>1 -> r7c8=1 -> r5c8=4
Now i need the "opposite" loop (from right to left), one of them must be true:
r5c8<>4 -> r7c8=4 -> r7c9=1 -> r5c9<>1 -> r5c38=13 -> r5c8<>4
(note, that r5c9<>1 -> r5c3<>3 is not true, because r5c3=3 -> r5c9=1 depends on r5c8=4).

Now we have:
r5c3=3 or r5c3=13 -> r5c3=13 (the one i already had above)
r5c8=4 or r5c8=13 -> r5c8=134
r7c8=1 or r7c8=4 -> r7c8=14
r5c9=1 or r7c9=1 -> r24c9<>1
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Postby daj95376 » Thu Apr 03, 2008 10:54 pm

Code: Select all
...3..71...6.5................1.73...85.........4......6..2...87.....4..1........ #44580

+--------------------------------------------------------------------------------------+
|  24589    2459     249     |  3        469      24689   |  7        1        24569   |
|  2489     17       6       |  2789     5        12489   |  289      23489    2349    |
|  24589    3        17      |  26789    14679    124689  |  25689    245689   24569   |
|----------------------------+----------------------------+----------------------------|
|  2469     249      249     |  1        689      7       |  3        245689   24569   |
|  3469     8        5       |  269      369      2369    |  169      4679     14679   |
|  2369     17       17      |  4        3689     5       |  2689     2689     269     |
|----------------------------+----------------------------+----------------------------|
|  459      6        349     |  579      2        1349    |  159      3579     8       |
|  7        259      2389    |  5689     1369     13689   |  4        23569    123569  |
|  1        2459     23489   |  56789    34679    34689   |  2569     235679   235679  |
+--------------------------------------------------------------------------------------+
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Postby eleven » Fri Apr 04, 2008 9:59 am

Nice puzzle for pencil&paper players ;)
Code: Select all
 *----------------------------------------------------------------------*
 | 24589  2459  249    | 3      469    24689   | 7      1       24569   |
 | 2489   17    6      | 2789   5      12489   | 289    23489   2349    |
 | 24589  3     17     | 26789 #14679  124689  | 25689  245689  24569   |
 |---------------------+-----------------------+------------------------|
 | 2469   249   249    | 1      689    7       | 3      245689  24569   |
 | 3469   8     5      | 269    369    2369    | 169    4679   #14679   |
 | 2369   17    17     | 4      3689   5       | 2689   2689    269     |
 |---------------------+-----------------------+------------------------|
 | 459    6     349    | 579    2      1349    | 159    3579    8       |
 | 7      259   2389   | 5689  #1369   13689   | 4      23569  #123569  |
 | 1      2459  23489  | 56789 #34679  34689   | 2569   235679 #235679  |
 *----------------------------------------------------------------------*
There are 2 overlapping skyscrapers for 1 and 7, one of r3c5 and r5c9 must be 1 and one of them 7.
Then also one of r8c5 and r8c9 must be 1 and one of r9c5 and r9c9 is 7.
I.e. r3c5=17, r5c9=17, r8c6<>1, r9c48<>7
Code: Select all
 *--------------------------------------------------------------------*
 |*24589 *2459 *249    | 3    #469    24689  | 7      1       24569   |
 |*2489   17    6      | 2789  5      12489  | 289    23489   2349    |
 |*24589  3     17     | 2689  17     24689  | 25689  245689  24569   |
 |---------------------+---------------------+------------------------|
 | 2469   249   249    | 1     689    7      | 3      245689  24569   |
 |#3469   8     5      | 269   369    2369   | 169   #4679   #17      |
 | 2369   17    17     | 4     3689   5      | 2689   2689    269     |
 |---------------------+---------------------+------------------------|
 | 459    6     349    | 579   2      1349   | 159    3579    8       |
 | 7      259   2389   | 5689  1369   3689   | 4      23569   123569  |
 | 1      2459  23489  | 5689 #34679  34689  | 2569   23569  #235679  |
 *--------------------------------------------------------------------*
Now to 4 an 7.
Skyscraper for 7 in rows 5 and 9, so one of r5c8 and r9c5 must be 7.
r5c8=7 -> r5c1=4 -> r1c23=4 -> r9c5=4
r9c5=7 -> r1c5=4 -> r23c1=4 -> r5c8=4
This also eliminates the 4's in r1c1, r1c69 and r47c1.
Then a ER eliminates 4 in r1c3.
Code: Select all
 *-------------------------------------------------------------------*
 | 2589   2459  29     | 3     469   2689   | 7      1       2569    |
 | 2489   17    6      | 2789  5     12489  | 289    23489   2349    |
 | 24589  3     17     | 2689  17    24689  | 25689  245689  24569   |
 |---------------------+--------------------+------------------------|
 | 269    249   249    | 1     689   7      | 3      245689  24569   |
 | 3469   8     5      | 269   369   2369   | 169    47      17      |
 | 2369   17    17     | 4     3689  5      | 2689   2689    269     |
 |---------------------+--------------------+------------------------|
 | 59     6     349    | 579   2     1349   | 159    3579    8       |
 | 7      259   2389   | 5689  1369  3689   | 4      23569   123569  |
 | 1      2459  23489  | 5689  47    34689  | 2569   23569   235679  |
 *-------------------------------------------------------------------*

r5c9=1 -> r3c5=7 -> r9c5=4
r8c9=1 -> r7c6=1 -> r7c3=4
i.e. r7c6<>4, r9c23<>4
Code: Select all
 *---------------------------------------------------------------*
 | 2589   459  29  | 3     469   2689   | 7      1       2569    |
 | 2489   17   6   | 2789  5     1289   | 289    23489   2349    |
 | 24589  3    17  | 2689  17    24689  | 25689  245689  24569   |
 |-----------------+--------------------+------------------------|
 | 269    49   29  | 1     689   7      | 3      245689  24569   |
 | 3469   8    5   | 269   369   2369   | 169    47      17      |
 | 2369   17   17  | 4     3689  5      | 2689   2689    269     |
 |-----------------+--------------------+------------------------|
 | 59     6    4   | 579   2     139    | 159    3579    8       |
 | 7      259  38  | 5689  1369  3689   | 4      23569   123569  |
 | 1      259  38  | 5689  47    34689  | 2569   23569   235679  |
 *---------------------------------------------------------------*
Either r5c9=1 or r5c9=7 -> r7c8=7 -> r7c6=3 -> r7c7=1, i.e. r5c7<>1
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Postby ronk » Fri Apr 04, 2008 1:39 pm

eleven wrote:There are 2 overlapping skyscrapers for 1 and 7, one of r3c5 and r5c9 must be 1 and one of them 7.
Then also one of r8c5 and r8c9 must be 1 and one of r9c5 and r9c9 is 7.
I.e. r3c5=17, r5c9=17, r8c6<>1, r9c48<>7

Nice find. In nice-loop notation ...

r3c5 =1= r8c5 -1- r8c9 =1= r5c9 =7= r9c9 -7- r9c5 =7= r3c5 =1= continuous loop
==> r3c5=17, r5c9=17,r8c6<>1, r9c48<>7
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Postby daj95376 » Fri Apr 04, 2008 5:55 pm

Yes, nice find eleven! FWIW, your results match a forcing chain on [r3c3].

I ran into several 17s that looked difficult, and then discovered they had an Achille's Heel that cracked them in one advanced step. Of the difficult looking 17s that I did post, others were able to crack them with one advanced step as well.

Does this mean that I finally ran across a 17 (outside of gsf's list) that requires more than one advanced step to crack?
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Postby ronk » Fri Apr 04, 2008 7:43 pm

daj95376 wrote:Does this mean that I finally ran across a 17 (outside of gsf's list) that requires more than one advanced step to crack?

Sure looks that way to me!
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Postby daj95376 » Sat Apr 05, 2008 1:06 am

As I mentioned earlier, eleven's results are equivalent to a forcing chain from [r3c3]. My (old) solver found a forcing net from [r3c3] that resulted in [r3c3]<>7. So, I kept looking for a way to extend the forcing chain from [r3c3] to produce a contradiction. I found it ... and then I found a shorter variant. Unfortunately, this results in one advanced step for this puzzle as well. Drat:(

Code: Select all
[r9c5]<>7 => simple SSTS solution to puzzle
[r9c5]= 7 [r5c9]=7 [r8c9]=1 [r7c47]=59 [r7c1]=4 [r1c23]=4 [r3c5]=4 => [c5]~1
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Postby daj95376 » Sat Apr 05, 2008 6:16 am

This is the only other 17 with 62 unresolved cells (in the PM) that might take more than one advanced step.

Code: Select all
2.......6.....1.3..5..4.....7...54..3...........6.....6..23....8..9...........1.. #26677

+--------------------------------------------------------------------------------------+
|  2        1348     13478   |  3578     5789     3789    |  578      14578    6       |
|  479      4689     46789   |  578      26       1       |  25789    3        245789  |
|  179      5        136789  |  378      4        26      |  2789     12789    12789   |
|----------------------------+----------------------------+----------------------------|
|  19       7        12689   |  138      289      5       |  4        2689     12389   |
|  3        124689   124689  |  1478     2789     24789   |  256789   256789   125789  |
|  5        12489    12489   |  6        2789     234789  |  23789    12789    123789  |
|----------------------------+----------------------------+----------------------------|
|  6        149      14579   |  2        3        478     |  5789     45789    45789   |
|  8        234      2457    |  9        1        47      |  23567    24567    23457   |
|  479      2349     23479   |  4578     5678     4678    |  1        2789     234789  |
+--------------------------------------------------------------------------------------+
daj95376
2014 Supporter
 
Posts: 2624
Joined: 15 May 2006

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