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au 3/5/12 tough

 
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Mon Mar 05, 2012 6:50 am    Post subject: au 3/5/12 tough Reply with quote
Code:
 *-----------*
 |...|3.6|.4.|
 |51.|...|...|
 |7..|2..|...|
 |---+---+---|
 |..9|8..|.21|
 |...|...|...|
 |24.|..9|3..|
 |---+---+---|
 |...|..8|..9|
 |...|...|.17|
 |.5.|1.3|...|
 *-----------*
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Tue Mar 06, 2012 3:44 pm    Post subject: Reply with quote
I had some time this morning and spent all of it chasing this "tough" puzzle. I can only assume that others will find a simpler, cleaner solution!

Code:
*-----------------------------------------------------------------------------*
 | 89      289     28      | 3       17      6       | 17      4       5       |
 | 5       1       346     | 479     4789    47      | 26789   6789    2368    |
 | 7       36      346     | 2       14589   145     | 1689    689     368     |
 |-------------------------+-------------------------+-------------------------|
 | 36      367     9       | 8       34567   457     | 467     2       1       |
 | 1368    3678    135678  | 467     123467  1247    | 46789   56789   468     |
 | 2       4       15678   | 67      167     9       | 3       5678    68      |
 |-------------------------+-------------------------+-------------------------|
 | 146     267     1267    | 4567    2467    8       | 2456    3       9       |
 | 34689   23689   2368    | 4569    2469    24      | 24568   1       7       |
 | 4689    5       2678    | 1       24679   3       | 2468    68      2468    |
 *-----------------------------------------------------------------------------*


anp (67=1)r6c45-(1=7)*r1c5-r79c5=r7c4-(7=6)r6c4; r45c5*<>7, r6c389<>6,b5q245<>6

almost SdC(24679)r789c5, ab =(67)r6c5, cd =(24)r8c6, e=(9)r89c5, fin=(1)r6c5
(1)r6c5-(1=7)*r1c5-als(47=9)r2c64; r2c5*<>7, r2c5,r8c4<>9

anp(15=8)r3c65-(5)r3c5=r4c5-(5=47)b5q34-(67=1)r6c45-r13c5=1r3c6; r2c7<>1

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Tue Mar 06, 2012 4:53 pm    Post subject: Reply with quote
I threw in the towel.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Tue Mar 06, 2012 8:01 pm    Post subject: Reply with quote
While preparing a "hint" for others to use, I ran across a solution that I hadn't expected to find.

Code:
 after basics
 +--------------------------------------------------------------------------------+
 |  89      289     28      |  3       17      6       |  17      4       5       |
 |  5       1       346     |  479     4789    47      |  26789   6789    2368    |
 |  7       36      346     |  2       14589   145     |  1689    689     368     |
 |--------------------------+--------------------------+--------------------------|
 |  36      367     9       |  8       34567   457     |  467     2       1       |
 |  1368    3678    135678  |  467     123467  1247    |  46789   56789   468     |
 |  2       4       15678   |  67      167     9       |  3       5678    68      |
 |--------------------------+--------------------------+--------------------------|
 |  146     267     1267    |  4567    2467    8       |  2456    3       9       |
 |  34689   23689   2368    |  4569    2469    24      |  24568   1       7       |
 |  4689    5       2678    |  1       24679   3       |  2468    68      2468    |
 +--------------------------------------------------------------------------------+
 # 148 eliminations remain

This solution is something that I noticed in the diagnostics output from my first solver. It made me think of Aligned Pair/Triple Exclusion logic. However, I haven't reviewed APE logic in some time, so I could easily be mistaken.

Code:
r23c6<>4; ( r2c6=7*, r1c5=1, r3c6=5* ); r4c6<>*57=4  =>  r58c6<>4


The reason I was running my first solver was to get this pattern:

Code:
 Hint: strong links including the (*) cells lead to a 4-SIS chain solution
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  5  |
 |  5  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  . *5 *5  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  . *5 *5  |  .  .  .  |
 |  .  .  5  |  .  .  .  |  .  5  .  |
 |  .  .  5  |  .  .  .  |  .  5  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  5  .  .  |  5  .  .  |
 |  .  .  .  |  5  .  .  |  5  .  .  |
 |  .  5  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Tue Mar 06, 2012 8:54 pm    Post subject: Reply with quote
Code:
 *-----------------------------------------------------------------------------*
 | 89      289     28      | 3      c17      6       | 17      4       5       |
 | 5       1       346     | 479     4789   b47      | 26789   6789    2368    |
 | 7       36      346     | 2       14589  d145     | 1689    689     368     |
 |-------------------------+-------------------------+-------------------------|
 | 36      367     9       | 8       34567   457     | 467     2       1       |
 | 1368    3678    135678  | 467     123467  1247    | 46789   56789   468     |
 | 2       4       15678   | 67      167     9       | 3       5678    68      |
 |-------------------------+-------------------------+-------------------------|
 | 146     267     1267    | 4567    2467    8       | 2456    3       9       |
 | 34689   23689   2368    | 4569    2469   a24      | 24568   1       7       |
 | 4689    5       2678    | 1       24679   3       | 2468    68      2468    |
 *-----------------------------------------------------------------------------*
(2=4)r8c6-(4=7)r2c6-(7=1)r1c5-(1)r3c6=(1)r5c6 =>r5c6<>2 stte
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
PostPosted: Tue Mar 06, 2012 8:55 pm    Post subject: Reply with quote
daj95376 wrote:
Code:
r23c6<>4; ( r2c6=7*, r1c5=1, r3c6=5* ); r4c6<>*57=4  =>  r58c6<>4

IOW : r1c5=1 or r1c5=7 => 4 in r234c6 => -4r58c6; stte

or, in Eureka notation :

(4=157)r234c6-(1=74)r1c5.r2c6 => -4r58c6; stte

PS : sotir's 4-SIS solution is based on the XW(5C56)
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Wed Mar 07, 2012 12:51 am    Post subject: Reply with quote
JC, my notation was a (feeble) attempt to reconstruct my recollection of APE logic. I do agree that your (implied) forcing network on r1c5 is simpler.

Code:
(1)r1c5 - (1=457)r234c6  =>  r58c6<>4
(7)r1c5 - (7=4  )r2  c6  =>  r58c6<>4
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ronk



Joined: 07 May 2006
Posts: 398
PostPosted: Wed Mar 07, 2012 1:32 am    Post subject: Reply with quote
daj95376 wrote:
This solution is something that I noticed in the diagnostics output from my first solver. It made me think of Aligned Pair/Triple Exclusion logic. However, I haven't reviewed APE logic in some time, so I could easily be mistaken.

Code:
r23c6<>4; ( r2c6=7*, r1c5=1, r3c6=5* ); r4c6<>*57=4  =>  r58c6<>4

You are correct.
Sudoku Explainer wrote:
Aligned Triplet Exclusion

The cells R1C5, R4C6 and R8C6 can together accept various combinations of values. But some combinations of values can be excluded, because they would leave some cells with no possible values.

More precisely, the following combinations of values are not possible for the cells R1C5, R4C6 and R8C6:
7, 7 and 4 because the cell R2C6 must already contain 4 or 7
1, 7 and 4 because the cell R2C6 must already contain 4 or 7
7, 5 and 4 because the cell R2C6 must already contain 4 or 7
1, 5 and 4 because the cell R3C6 must already contain 1, 4 or 5
7, 4 and 4 because the same value cannot occur twice in the same row, column or block
1, 4 and 4 because the same value cannot occur twice in the same row, column or block

Because some potential values of R8C6 occur in none of the remaining combinations, they can safely be removed.

The subsuming als-xz is certainly easier to understand.
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