remote triples

Advanced methods and approaches for solving Sudoku puzzles

Postby PIsaacson » Mon Oct 27, 2008 1:06 pm

Dear StrmCkr,

Forgive me in advance for asking here:

Is your constraint theory similar to subset counting, or more like Allan Barker's base/cover link-set logic (which I'm still trying to comprehend). Thanks to working on distributed-disjoint-subsets, which you greatly helped me with suggestions/advice, subset counting at least makes sense to me from a programming pov. Trying to figure out how to find all base/cover sets of (what seems like) potentially anything gives me headaches.
PIsaacson
 
Posts: 249
Joined: 02 July 2008

Postby udosuk » Thu Oct 30, 2008 7:05 pm

ronk wrote:
udosuk wrote:
Code: Select all
+----------+----------+-------------------+
|  .  .  . |  .  .  . |  .    .     .     |
|  .  .  . |  .  X  . |  .    29    .     |
|  .  .  . |  .  .  . |  .    .     .     |
+----------+----------+-------------------+
|  .  .  . |  .  .  . | .     12589 .     |
|  .  .  . |  .  29 . | 12589 12589 12589 |
|  .  .  . |  .  .  . | .     12589 .     |
+----------+----------+-------------------+
|  .  .  . |  .  .  . |  .    .     .     |
|  .  .  . |  .  .  . |  .    .     .     |
|  .  .  . |  .  .  . |  .    .     .     |
+----------+----------+-------------------+
X <> 2,9

(The mechanism is similar to Empty Rectangle but not quite the same.)

If there is no ER, where is your strong link:?:

The grouped strong link is at r46c8+r5c789 (or alternatively, r456c8+r5c79), which disallows r2c8+r5c5 to be both 2s or both 9s, thus eliminating r2c5 from being 2 or 9.

Compared to the following ER:
Code: Select all
+----------+----------+-------------------+
|  .  .  . |  .  .  . |  .    .     .     |
|  .  .  . |  .  29 . |  .    Y     .     |
|  .  .  . |  .  .  . |  .    .     .     |
+----------+----------+-------------------+
|  .  .  . |  .  .  . | .     12589 .     |
|  .  .  . |  .  29 . | 12589 12589 12589 |
|  .  .  . |  .  .  . | .     12589 .     |
+----------+----------+-------------------+
|  .  .  . |  .  .  . |  .    .     .     |
|  .  .  . |  .  .  . |  .    .     .     |
|  .  .  . |  .  .  . |  .    .     .     |
+----------+----------+-------------------+
Y <> 2,9

Alternatively, we can view the ER above as a grouped turbot fish:

Grouped strong link: r456c8+r5c79 must have 2
Strong link: r25c5 must have 2
Weak link: r5c5 & r5c79 can't both contain 2
If r5c5<>2, r2c5=2
If r5c79<>2, r456c8 have 2
=> r2c8 can't be 2

Same argument on digit 9.

:idea:
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby daj95376 » Thu Oct 30, 2008 7:18 pm

My guess is that udosuk is talking in terms of the classic Empty Rectangle solving technique, and ronk is thinking in terms of the Empty Rectangle pattern. Apples and oranges!!!
daj95376
2014 Supporter
 
Posts: 2624
Joined: 15 May 2006

Postby ronk » Fri Oct 31, 2008 2:39 am

udosuk wrote:The grouped strong link is at r46c8+r5c789 (or alternatively, r456c8+r5c79), which disallows r2c8+r5c5 to be both 2s or both 9s, thus eliminating r2c5 from being 2 or 9.

Thanks, I finally see your POV. For a locked set ("LS"), all candidates must ultimately be placed exactly once. That makes for an interesting nice loop expression:

r2c5 -2- r5c5 -9- LS:(r5c789 =9|1458|9= r456c8) -9- r2c8 -2- r2c5 ==> r2c5<>2

Note: To be read right-to-left also, r5c8 is included twice.

Personally, I would just apply the locked set in box 6, and use the resultant ERs in two w-wings ... as (I believe) you suggested earlier.
ronk
2012 Supporter
 
Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Postby udosuk » Fri Oct 31, 2008 4:49 pm

ronk, I see your usage of "locked set" in here but it's not the necessary condition - you only need the two candidates (2 & 9) to be locked in those 5 cells as a condition.

For example, the following also works:
Code: Select all
+----------+----------+-------------------------------+
|  .  .  . |  .  .  . |  .        .         .         |
|  .  .  . |  .  X  . |  .        29        .         |
|  .  .  . |  .  .  . |  .        .         .         |
+----------+----------+-------------------------------+
|  .  .  . |  .  .  . | 1345678   123456789 1345678   |
|  .  .  . |  .  29 . | 123456789 123456789 123456789 |
|  .  .  . |  .  .  . | 1345678   123456789 1345678   |
+----------+----------+-------------------------------+
|  .  .  . |  .  .  . |  .        .         .         |
|  .  .  . |  .  .  . |  .        .         .         |
|  .  .  . |  .  .  . |  .        .         .         |
+----------+----------+-------------------------------+
X <> 2,9

:idea:
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby StrmCkr » Fri Oct 31, 2008 5:34 pm

ronk, I see your usage of "locked set" in here but it's not the necessary condition - you only need the two candidates (2 & 9) to be locked in those 5 cells as a condition


correct

heres a hybrids with more degernation.

Code: Select all
 *-----------------------------*
 | . . . | . .  . | .   .    . |
 | . . . | . X  . | .   29   . |
 | . . . | . .  . | .   .    . |
 |-------+--------+------------|
 | . . . | . .  . | .   289  . |
 | . . . | . 29 . | 289 8-9    . |
 | . . . | . .  . | .   .   . |
 |-------+--------+------------|
 | . . . | . .  . | .   .    . |
 | . . . | . .  . | .   .    . |
 | . . . | . .  . | .   .    . |
 *------------------------------*


the x is still removed as 29's and R5C8 aslo <>9
Last edited by StrmCkr on Fri Oct 31, 2008 2:51 pm, edited 2 times in total.
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 625
Joined: 05 September 2006

Postby udosuk » Fri Oct 31, 2008 6:04 pm

StrmCkr, as usual I think you're making things way more complicated than they should be.:(

StrmCkr wrote:
Code: Select all
 *-----------------------------*
 | . . . | . .  . | .   .    . |
 | . . . | . X  . | .   29   . |
 | . . . | . .  . | .   .    . |
 |-------+--------+------------|
 | . . . | . .  . | .   289  . |
 | . . . | . 29 . | 289 8-9    . |
 | . . . | . .  . | .   .   . |
 |-------+--------+------------|
 | . . . | . .  . | .   .    . |
 | . . . | . .  . | .   .    . |
 | . . . | . .  . | .   .    . |
 *------------------------------*

the x is still removed as 29's and R5C8 aslo <>9

It is in fact just a simple intersection/locked candidate elimination:
8 @ r5,b6 locked @ r5c78
Naked pair: r24c8={29}
=> r5c8<>9

StrmCkr wrote:
Code: Select all
 *-----------------------------*
 | . . . | . .  . | .   .    . |
 | . . . | . X  . | .   29   . |
 | . . . | . .  . | .   .    . |
 |-------+--------+------------|
 | . . . | . .  . | .   289  . |
 | . . . | . 29 . | 28 89    . |
 | . . . | . .  . | .   .   . |
 |-------+--------+------------|
 | . . . | . .  . | .   .    . |
 | . . . | . .  . | .   .    . |
 | . . . | . .  . | .   .    . |
 *------------------------------*

this one degernates completly

8 @ c8,b6 locked @ r45c8
=> r5c578=[928]
=> r24c8=[29]

:idea:
Last edited by udosuk on Fri Oct 31, 2008 2:06 pm, edited 1 time in total.
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby ronk » Fri Oct 31, 2008 6:06 pm

udosuk wrote:you only need the two candidates (2 & 9) to be locked in those 5 cells as a condition.

Then it's already an ER.

Either you know it's an ER or you don't; make up your mind.
ronk
2012 Supporter
 
Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Postby udosuk » Fri Oct 31, 2008 6:12 pm

ronk wrote:
udosuk wrote:you only need the two candidates (2 & 9) to be locked in those 5 cells as a condition.

Then it's already an ER.

Either you know it's an ER or you don't; make up your mind.

The pattern in the block (b6 here) has the same pattern as an ER (namely r46c79 doesn't contain the two candidates involved), but the actual elimination mechanisms are different. In the (classical) ER, e.g. you use the strong link @ r25c5 (if there is one) to eliminate the candidate(s) from r2c8. In this move however you use the fact that r2c8+r5c5 are both from {29} to eliminiate the candidates from r2c5.

I think you need to distinguish between ER as a solving technique or a pattern.
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby ronk » Fri Oct 31, 2008 6:18 pm

udosuk wrote:I think you need to distinguish between ER as a solving technique or a pattern.

You can think what you want ... but I'm done with this word game.
ronk
2012 Supporter
 
Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Postby StrmCkr » Thu Dec 18, 2008 5:28 pm

alirghty i found one for udosuks examples from the top1465
#129

Code: Select all
 *-----------*
 |.13|5..|...|
 |...|.7.|4..|
 |...|...|...|
 |---+---+---|
 |1..|...|.89|
 |2.4|.6.|...|
 |7..|...|...|
 |---+---+---|
 |.8.|1..|...|
 |6..|...|2..|
 |...|9.3|...|
 *-----------*


Code: Select all
 *-----------------------------------------------------------------------------*
 | 48      1       3       | 5       9       248     | 78      267     2678    |
 | 589     256     256     | 268     7       128     | 4       12359   12358   |
 | 4589    24567   2567    | 2468    3       1248    | 1589    1259    1258    |
 |-------------------------+-------------------------+-------------------------|
 | 1       36-5    56      | 247     45@     2457    | 3567    8       9       |
 | 2       359     4       | 78      6       5789    | 1357    157     157     |
 | 7       569     8       | 3       1       59      | 56      24      24      |
 |-------------------------+-------------------------+-------------------------|
 | 3       8       279     | 1       245@    6       | 579     4579    457     |
 | 6       45@     19      | 47@      8       57@     | 2       139     13      |
 | 45      27      127     | 9       245@    3       | 1578    14567   145678  |
 *-----------------------------------------------------------------------------*
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 625
Joined: 05 September 2006

Previous

Return to Advanced solving techniques