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Puzzle 11/08/21: ~ XY

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sun Aug 21, 2011 6:32 pm    Post subject: Puzzle 11/08/21: ~ XY Reply with quote

Code:
 +-----------------------+
 | . . 4 | 5 . 6 | . 9 8 |
 | . . 2 | 4 . . | . . 7 |
 | 6 7 5 | . . . | . . 4 |
 |-------+-------+-------|
 | 9 5 . | 6 8 . | . . 3 |
 | . . . | 7 3 . | . . . |
 | 7 . . | . . 9 | . . . |
 |-------+-------+-------|
 | . . . | . . . | 9 . 2 |
 | 3 . . | . . . | . 4 . |
 | 5 2 9 | 3 . . | 8 . . |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Mon Aug 22, 2011 4:40 am    Post subject: Reply with quote

XY-Chain. 6 in r9c5 proves 4 in r4c6; r6c5<>4
Skyscraper; r6c9, r8c7<>1
W-Wing (56), SL 5 in r8; r56c7<>6
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Mon Aug 22, 2011 1:50 pm    Post subject: Reply with quote

I finally found some time for Sudoku. Very Happy

Two solutions; a one stepper and a two stepper.

aur(29)r38c45 external sis: r3c6=2, r8c6=2; r4c6<>2

or

axy-wing(24-1)[r49c6+r6c4]=(7)r9c6-r9c8=r8c7-(7=4)r4c7-(4=2)r4c6-(2=1)r6c4; r5c6,r78c4<>1
Type 1 UR(29)r38c45; r8c5<>29=6

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Aug 22, 2011 5:45 pm    Post subject: Reply with quote

Aaaagh!!! I really need to add external SIS logic to my UR() routine.

Nice find, Ted.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Mon Aug 22, 2011 9:32 pm    Post subject: Reply with quote

daj95376 wrote:
I really need to add external SIS logic to my UR() routine.

Nice find, Ted.

tlanglet, I second the nice find.

daj95376, Ted's AUR would be destroyed by a co-existent "UR+3C/2SL" for r8c4<>2.

here Mike Barker wrote:
Code:
--- UR+3C/2SL: both strong links share a node, do not include the bivalue cell and have equal labels => "b" can be removed from "abZ"

 ab     abX
         |
        a|
     a   |
abY-----abZ

How would you avoid that in your solver?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Aug 23, 2011 3:37 am    Post subject: Reply with quote

ronk wrote:
daj95376, Ted's AUR would be destroyed by a co-existent "UR+3C/2SL" for r8c4<>2.

Code:
Mike Barker--- UR+3C/2SL: both strong links share a node, do not include the bivalue cell and have equal labels => "b" can be removed from "abZ"

 ab     abX
         |
        a|
     a   |
abY-----abZ

How would you avoid that in your solver?

That UR elimination is one of two found by my solver.

Code:
 +--------------------------------------------------------------+
 |  1     3     4     |  5     7     6     |  2     9     8     |
 |  8     9     2     |  4     1     3     |  56    56    7     |
 |  6     7     5     |  289   29    28    |  3     1     4     |
 |--------------------+--------------------+--------------------|
 |  9     5     1     |  6     8     24    |  47    27    3     |
 |  2     468   68    |  7     3     145   |  1456  568   9     |
 |  7     468   3     |  12    245   9     |  1456  2568  156   |
 |--------------------+--------------------+--------------------|
 |  4     168   678   |  18    56    1578  |  9     3     2     |
 |  3     168   678   |  1289  269   1278  |  1567  4     156   |
 |  5     2     9     |  3     46    147   |  8     67    16    |
 +--------------------------------------------------------------+
 # 63 eliminations remain

 r38c45  <29> UR via s-link              <> 2    r8c4
 r25c78  <56> UR via s-link + N_Singles  <> 6    r5c7
 <s list-only>

Code:
 after r8c4<>2 from strong links UR logic
 +--------------------------------------------------------------+
 |  1     3     4     |  5     7     6     |  2     9     8     |
 |  8     9     2     |  4     1     3     |  56    56    7     |
 |  6     7     5     |  289   29    28    |  3     1     4     |
 |--------------------+--------------------+--------------------|
 |  9     5     1     |  6     8     24    |  47    27    3     |
 |  2     468   68    |  7     3     145   |  1456  568   9     |
 |  7     468   3     |  12    245   9     |  1456  2568  156   |
 |--------------------+--------------------+--------------------|
 |  4     168   678   |  18    56    1578  |  9     3     2     |
 |  3     168   678   |  189   269   1278  |  1567  4     156   |
 |  5     2     9     |  3     46    147   |  8     67    16    |
 +--------------------------------------------------------------+
 # 62 eliminations remain

However, that wouldn't prohibit my solver from continuing with the potential <29> UR.

Awhile back, I re-wrote all of my UR routines to rely on finding an X-pattern in two digits (under UR conditions). The potential UR condition would still be detected because this pattern of candidates still remain.

Code:
 X-pattern in {2,9}
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  2  9  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  9  2  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

In fact, thats how my solver detects a UR Type 1.1 elimination where three of the cells are solved and an elimination exists in the fourth cell.

Code:
 UR Type 1.1  =>  r3c5<>b
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  a  bX .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  b  a  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


Regards, Danny
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Ertekaz



Joined: 28 Aug 2013
Posts: 1

PostPosted: Wed Aug 28, 2013 3:59 am    Post subject: Reply with quote

Never understand Yet
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