Contrary "17" Puzzles

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

Postby Draco » Wed May 21, 2008 3:48 am

daj95376 wrote:
Code: Select all
 ..6..3....1.....4.....5....2.....3...9.1.....5.........8....1.93...2.......4...5. #46801

After SSTS apply this net:

r7c3=2 r7c1=4 [r1c1<>4] r1c2=4 [r1c2<>2] + [r9c2<>2] => r3c2=2 r3c8=3 ... and ...
r7c8=2 r3c8=3
So: r3c2<>3, r3c8 = 3, r7c8<>3

SSTS to solve.

Cheers...

- drac

[edit - fixed typo]
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Postby daj95376 » Tue May 27, 2008 7:28 am

I'm posting this here because of the source of the puzzle.

My solver appears to now handle a subset of chains. Unfortunately, side-effect eliminations for continuous loops aren't included. Consider the following puzzle and chain for the PM.

Code: Select all
 .......14......2.38...5.......2.7....31............65.6.....7.....14.......3..... #28

 +--------------------------------------------------------------------------------+
 |  2379    2679    23679   |  6789    23689   2389    |  5       1       4       |
 |  14579   145679  45679   |  679     169     19      |  2       8       3       |
 |  8       12      23      |  4       5       123     |  9       67      67      |
 |--------------------------+--------------------------+--------------------------|
 |  459     45689   45689   |  2       189     7       |  1348    349     189     |
 |  2479    3       1       |  5689    689     4589    |  48      2479    2789    |
 |  2479    24789   24789   |  89      1389    13489   |  6       5       12789   |
 |--------------------------+--------------------------+--------------------------|
 |  6       124589  234589  |  589     289     2589    |  7       2349    12589   |
 |  23579   25789   235789  |  1       4       25689   |  38      2369    25689   |
 |  12459   124589  24589   |  3       7       25689   |  148     2469    125689  |
 +--------------------------------------------------------------------------------+

Code: Select all
[r4c7]=1=[r9c7]-1-[r9c1]=1=[r2c1]-1-[r3c2]=1=[r3c6]=3=[r3c3]-3-[r7c3]=3=[r7c8]-3-[r4c8]=3=[r4c7]

The obvious eliminations are:

Code: Select all
=> [r4c7]<>48

However, I manually found the following side-effect eliminations:

Code: Select all
=> [r9c29]<>1, [r2c2]<>1, [r18c3]<>3, [r8c8]<>3

Are my eliminations correct? Are there eliminations that I missed?

TIA:!::!::!:
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Postby ronk » Tue May 27, 2008 11:34 am

daj95376 wrote:
Code: Select all
[r4c7]=1=[r9c7]-1-[r9c1]=1=[r2c1]-1-[r3c2]=1=[r3c6]=3=[r3c3]-3-[r7c3]=3=[r7c8]-3-[r4c8]=3=[r4c7]
...
=> [r4c7]<>48
...
=> [r9c29]<>1, [r2c2]<>1, [r18c3]<>3, [r8c8]<>3

Are my eliminations correct? Are there eliminations that I missed?

Nice continuous-nice-loop! The eliminations you have are correct, but you're missing one.

Knowing there is one missing, you should be able to find it. Hint: Due to the continuous property of the loop, all weak inferences are converted to conjugate inferences.
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Postby daj95376 » Tue May 27, 2008 4:23 pm

ronk wrote:The eliminations you have are correct, but you're missing one.

Okay, adding [r3c6]<>2 to my list. Thanks ronk!
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Postby daj95376 » Tue May 27, 2008 10:20 pm

Code: Select all
 3..1.7....2....8..............3...47.8..6...........1.1.7...3.....52....4........ #29329

 +-----------------------------------------------------------------------------------------+
 |  3        469      45689    |  1        4589     7        |  2459     2569     24569    |
 |  5679     2        14569    |  469      3459     34569    |  8        35679    134569   |
 |  56789    14679    145689   |  24689    34589    2345689  |  14579    35679    134569   |
 |-----------------------------+-----------------------------+-----------------------------|
 |  2569     169      1569     |  3        1589     12589    |  2569     4        7        |
 |  2579     8        1459     |  2479     6        12459    |  259      2359     2359     |
 |  25679    34679    34569    |  2479     4579     2459     |  2569     1        8        |
 |-----------------------------+-----------------------------+-----------------------------|
 |  1        569      7        |  4689     489      4689     |  3        25689    24569    |
 |  689      369      3689     |  5        2        13469    |  1479     679      1469     |
 |  4        3569     2        |  6789     13789    13689    |  159      5689     569      |
 +-----------------------------------------------------------------------------------------+
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Postby daj95376 » Tue May 27, 2008 10:58 pm

Code: Select all
 ......1.94...5........2.3.....1.9...5....7......3......13.......8.....4...9....2. #929

 +--------------------------------------------------------------------------------+
 |  38      23567   2678    |  4678    37      3468    |  1       5678    9       |
 |  4       3679    1678    |  6789    5       1368    |  2678    678     2678    |
 |  19      5679    1678    |  6789    2       168     |  3       5678    4       |
 |--------------------------+--------------------------+--------------------------|
 |  38      2367    24678   |  1       468     9       |  245678  3678    25678   |
 |  5       369     1468    |  2       468     7       |  4689    13689   68      |
 |  19      2679    124678  |  3       468     5       |  246789  16789   2678    |
 |--------------------------+--------------------------+--------------------------|
 |  267     1       3       |  45678   79      2468    |  56789   6789    5678    |
 |  267     8       5       |  67      1379    236     |  679     4       13      |
 |  67      4       9       |  5678    137     368     |  5678    2       13      |
 +--------------------------------------------------------------------------------+
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Postby Draco » Wed May 28, 2008 12:11 am

Solution to #929 (from PM's):

r6c1=1 [r6c8<>1] r5c8=1 r5c2=3 + r6c1=9 => r5c2<>9

You can clear a Locked Set & XY-Wing if you like or not.. this solution skips that at the expense of adding 1 link to the second chain that follows:

r1c5=3 r1c1=8 r4c1=3 r5c2=6 r5c8=3 +
r1c5=7 r7c5=9 r8c7=9 [r5c7<>9] r5c8=9 => r5c8<>168

Singles to solve.

Cheers...

- drac
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Postby daj95376 » Thu May 29, 2008 6:28 pm

Carcul wrote:
Code: Select all
 *------------------------------------------------------------------------*
 | 6789    3789    1     | 2379    2679    23679  | 3679    4       5     |
 | 2       3479    35679 | 3479    8       345679 | 13679   1369    13679 |
 | 45679   3479    35679 | 3479    1       345679 | 3679    28      28    |
 |-----------------------+------------------------+-----------------------|
 | 46789   24789   6789  | 5       3       1      | 4679    269     24679 |
 | 3       14      56    | 279     279     279    | 8       156     146   |
 | 1579    1279    579   | 6       4       8      | 13579   12359   12379 |
 |-----------------------+------------------------+-----------------------|
 | 789     5       4     | 1       2679    23679  | 369     3689    3689  |
 | 189     6       2     | 3489    59      349    | 13459   7       13489 |
 | 1789    13789   3789  | 4789    5679    4679   | 2       15689   14689 |
 *------------------------------------------------------------------------*

1) [r8c7]=5=[r6c7]-5-[r6c1]=5=[r3c1]=4=[r4c1](-4-[r5c2]-1-[r6c1])-4-
-[r4c7]=4=[r8c7], => r8c7<>1,3,9; r6c3, r6c8<>5; r3c1<>6,7,9; r6c1<>1; r4c2, r4c9<>4.

2) [r4c2]=2=[r6c2]=1=[r5c2]=4=[r4c1](=6=[r1c1]=8=[r1c2]-8-[r4c2])-
-4-[r3c1]-5-[r6c13]-7,9-[r46c2], => r4c2, r6c2<>7,9; r4c2<>8, and the puzzle is solved.

Carcul's side-effect of [r6c1]<>1 had me confused at first. Then I discovered a side-effect that appears to have been overlooked -- [r9c2]<>1.

Either, ...

Code: Select all
[r6c1]=5 => [r56c2]=1 => [r9c2]<>1   -or-
[r4c1]=4 => [r5 c2]=1 => [r9c2]<>1

BTW: Did I happen to mention that continuous loops make my head go TILT:D
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Postby daj95376 » Fri May 30, 2008 6:10 am

[Edit: Discarded because my bookeeping sucks!!!]
Last edited by daj95376 on Fri May 30, 2008 11:50 am, edited 1 time in total.
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Postby eleven » Fri May 30, 2008 9:14 am

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Postby daj95376 » Fri May 30, 2008 3:51 pm

Thanks eleven for catching my mistake. I withdrew the puzzle.
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Postby daj95376 » Sat May 31, 2008 4:35 am

I found a JPF statistical table listing the SE difficulty distribution for the first 47K "17" puzzles. It also listed a sample puzzle number from each rating group. So, I decided it was best to examine entries above 47K. This one seems to qualify as contrary.

Code: Select all
..4...53..8..6........1....1..5..7..2.......6.....8....3.4...8.6..1.............. #47137

 +--------------------------------------------------------------+
 |  79    6     4     |  8     279   279   |  5     3     1     |
 |  379   8     1     |  379   6     5     |  4     279   279   |
 |  3579  2     579   |  379   1     4     |  8     6     79    |
 |--------------------+--------------------+--------------------|
 |  1     9     6     |  5     234   23    |  7     24    8     |
 |  2     57    8     |  79    479   1     |  3     459   6     |
 |  4     57    3     |  6     279   8     |  29    1     259   |
 |--------------------+--------------------+--------------------|
 |  579   3     2579  |  4     579   6     |  1     8     2579  |
 |  6     4     2579  |  1     8     79    |  29    2579  3     |
 |  8     1     579   |  2     3579  379   |  6     579   4     |
 +--------------------------------------------------------------+
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Postby hobiwan » Sat May 31, 2008 3:31 pm

#29329:

Forcing Net Contradiction in [r7c8] => [r5c6]=1
[r5c6]<>1=>[r5c3]=1(=>[r2c3]<>1)=>[r3c3]<>1=>[r3c2]=1=>[r3c2]<>7=>[r6c2]=7(=>[r6c2]<>4)=>[r6c2]<>3=>[r6c3]=3=>[r6c3]<>4=>[r5c3]=4=>[r5c3]<>1=>[r5c6]=1
Skyscraper + W-Wing

A nice nice loop for daj95376:
Continuous Nice Loop [r4c2]=1=[r3c2]=7=[r6c2]-7-[r6c5]=7=[r9c5]=1=[r4c5]-1-[r4c2] => [r4c36]<>1, [r9c5]<>389, [r3c2]<>469, [r6c14]<>7
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Postby hobiwan » Sat May 31, 2008 3:46 pm

#929:
Uniqueness Test 3: 1/3 in [r8c59],[r9c59] => [r1c5],[r789c4]<>7
(Locked Pair in r789c5 {79})
Singles

Or:
Uniqueness Test 4: 1/3 in [r8c59],[r9c59] => [r89c5]<>3
Singles

If you don't like Uniqueness, there are plenty of possibilities, e.g.:
Forcing Chain Contradiction in r5 => [r6c8]=1
[r6c8]<>1=>[r5c8]=1=>[r5c2]=3=>[r5c2]<>9
[r6c8]<>1=>[r5c8]=1=>[r5c2]=3=>[r2c6]=3=>[r1c5]=7=>[r7c5]=9=>[r8c7]=9=>[r5c7]<>9
[r6c8]<>1=>[r5c8]=1=>[r5c8]<>9
Singles

I tried to find an alternative to UR Type 3 (r1c5<>8), but the only thing I could find was not very pretty:
Forcing Net Verity => [r1c5]=3
[r2c3]=1=>[r5c3]<>1=>[r5c8]=1(=>[r5c8]<>9)=>[r5c8]<>3=>[r5c2]=3=>[r5c2]<>9=>[r5c7]=9(=>[r7c7]<>9)=>[r8c7]<>9=>[r7c8]=9=>[r7c5]<>9=>[r7c5]=7=>[r1c5]<>7=>[r1c5]=3
[r2c6]=1=>[r2c6]<>3=>[r2c2]=3=>[r5c2]<>3=>[r5c8]=3(=>[r5c8]<>9)=>[r5c8]<>1=>[r6c8]=1=>[r6c8]<>9=>[r7c8]=9=>[r7c5]<>9=>[r7c5]=7=>[r1c5]<>7=>[r1c5]=3
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Postby hobiwan » Sat May 31, 2008 4:22 pm

#47137: This is a tough one!

One possibility:

Forcing Net Verity => [r3c1]=5
[r6c5]=2=>[r4c6]=3=>[r9c5]=3=>[r7c5]=5=>[r3c1]=5
[r6c5]=7=>[r6c2]=5=>[r7c9]=5=>[r3c1]=5
[r6c5]=9(=>[r9c5]<>9)(=>[r7c5]<>9)=>[r8c7]=9=>[r9c6]=9=>[r9c5]=3=>[r7c5]=5=>[r3c1]=5
After that a Remote Pair, Sashimi X-Wing, XY-Wing and Skyscraper

Alternative: Forcing Net (see above) plus Singles, then:
Sashimi X-Wing: 7 c16 r17 f[r8c6] f[r9c6] => [r7c5]<>7
Sashimi X-Wing: 9 c16 r17 f[r8c6] f[r9c6] => [r7c5]<>9
After that Singles plus 1 Remote Pair

[edit: changed the whales to x-wings, see below]

Completely different route:

Forcing Net Contradiction in [r7c1] => [r6c2]=7
[r6c2]<>7=>[r6c2]=5=>[r7c9]=5=>[r7c1]<>5
[r6c2]<>7(=>[r6c5]=7=>[r7c5]<>7)=>[r6c2]=5=>[r7c9]=5=>[r7c5]=9(=>[r8c6]<>9)=>[r1c6]=9=>[r1c1]=7=>[r7c1]<>7
[r6c2]<>7(=>[r6c5]=7=>[r7c5]<>7)=>[r6c2]=5=>[r7c9]=5=>[r7c5]=9=>[r7c1]<>9
Full House: [r5c2]=5
Hidden Single: [r6c9]=5
Forcing Net Verity => [r3c1]=5
[r4c6]=2=>[r6c7]=2=>[r8c7]=9(=>[r8c6]<>9=>[r8c6]=7=>[r7c5]<>7)=>[r6c5]=9=>[r7c5]=5=>[r3c1]=5
[r4c6]=3=>[r9c5]=3=>[r7c5]=5=>[r3c1]=5
Singles plus Remote Pair
Last edited by hobiwan on Tue Jun 03, 2008 3:03 pm, edited 1 time in total.
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