The New Sudoku Players' Forum

by **StrmCkr** » Fri Oct 24, 2008 2:50 pm

Remote Triples: {unsure if this is new or not..}

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

X < > 2,9

Side note: from standard locked set operand.
R5C7 < > 8,

Which shows this self-degenerated variation of this same type:

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

X<>2,9

A real world example:

Code: Select all: *-----------* |...|.5.|.6.| |17.|6..|5..| |9.6|3..|.18| |---+---+---| |...|..1|..5| |.41|..6|.73| |2..|...|...| |---+---+---| |7..|...|.3.| |.2.|.8.|.4.| |.39|...|.5.| *-----------*

Code: Select all: *-----------------------------------------------------------------------------* | 348 8 2348 | 124789 5 24789 | 23479 6 2479 | | 1 7 2348 | 6 4-29 2489 | 5 29@ 249 | | 9 5 6 | 3 247 247 | 247 1 8 | |-------------------------+-------------------------+-------------------------| | 368 689 378 | 24789 23479 1 | 24689 289@ 5 | | 58 4 1 | 2589 29@ 6 | 29-8@ 7 3 | | 2 5689 3578 | 45789 3479 345789 | 14689 89@ 1469 | |-------------------------+-------------------------+-------------------------| | 7 1568 458 | 12459 12469 2459 | 12689 3 1269 | | 56 2 5 | 1579 8 3579 | 1679 4 1679 | | 468 3 9 | 1247 12467 247 | 12678 5 1267 | *-----------------------------------------------------------------------------*

R2C5 <>2,9, R5C7 <>8

edit
i noticed there is some additional restrictiosn from this chain as well..

Code: Select all: *-----------------------------* | . . . | . . . | . . . | | . . . | . X . | . 29 . | | . . . | . . . | . . . | |-------+--------+------------| | . . . | . . . | / 289 / | | x x x | x 29 x | 289 / / | . . . | . . . | / 89 / | |-------+--------+------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *------------------------------*

mostly from the pair that is derived in the process.

Website · by **denis_berthier** » Fri Oct 24, 2008 10:04 pm

StrmCkr wrote:Remote Triples: {unsure if this is new or not..}

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

X < > 2,9

xyt-chain {2 9}r2c8 - {9 8}r6c8 - {8 2 9#1}r5c7 - {2 9 8#2}r4c8 - {9 2}r5c5 ==> r2c5 <> 2

and a similar chain for r2c5 <> 9, once one has eliminated r5c7 <> 8

[Corrected an error noticed by ronk in the first version of this chain]

by **PIsaacson** » Sat Oct 25, 2008 10:05 am

StrmCkr,

Thanks for the updates!

Allan's link-sets and Champagne's full-tagging are on my "must-read, must-try-to-understand" list. I've read their posts, gone to their web sites and I have a notebook full of questions and high level designs to duplicate some of their work. I even wrote a small program to find all possible sets/link-sets to determine approximate computation time. The "average" puzzle takes over 48 hours, and that's without any logic to combine them into base/cover link-sets with associated reductions. I'm looking forward to your constraint approach. Send me the url/topic.

My solver determined that your remote triples was best solved by POM.

Code: Select all: Puzzle: ....5..6.17.6..5..9.63...18.....1..5.41..6.732........7......3..2..8..4..39....5. puzzle 1 ../test/remote_triples.ss 348 8 2348 |124789 5+ 24789 |23479 6+ 2479 1+ 7+ 2348 |6+ 249 2489 |5+ 29 249 9+ 5 6+ |3+ 247 247 |247 1+ 8+ --------- --------- ---------+--------- --------- ---------+--------- --------- --------- 368 689 378 |24789 23479 1+ |24689 289 5+ 58 4+ 1+ |2589 29 6+ |289 7+ 3+ 2+ 5689 3578 |45789 3479 345789 |14689 89 1469 --------- --------- ---------+--------- --------- ---------+--------- --------- --------- 7+ 1568 458 |12459 12469 2459 |12689 3+ 1269 56 2+ 5 |1579 8+ 3579 |1679 4+ 1679 468 3+ 9+ |1247 12467 247 |12678 5+ 1267 do_pinnings - starting with 27 total solved update_cell - setting r1c2 = d8 update_cell - setting r1c4 = d1 update_cell - setting r1c7 = d3 update_cell - setting r2c3 = d3 update_cell - setting r2c6 = d8 update_cell - setting r3c2 = d5 update_cell - setting r4c1 = d3 update_cell - setting r6c5 = d3 update_cell - setting r7c2 = d1 update_cell - setting r8c3 = d5 update_cell - setting r8c6 = d3 update_cell - setting r9c5 = d1 do_pinnings - ending with 12 updates 39 total solved do_pinnings - starting with 39 total solved update_cell - setting r1c1 = d4 update_cell - setting r1c3 = d2 update_cell - setting r5c1 = d5 update_cell - setting r7c3 = d4 update_cell - setting r7c5 = d6 update_cell - setting r7c7 = d8 update_cell - setting r8c1 = d6 update_cell - setting r9c1 = d8 do_pinnings - ending with 8 updates 47 total solved do_pinnings - starting with 47 total solved update_cell - setting r5c4 = d8 do_pinnings - ending with 1 updates 48 total solved do_pinnings - starting with 48 total solved do_pinnings - ending with 0 updates 48 total solved do_restrictions - starting with 48 total solved do_restrictions - ending with 0 updates 48 total solved do_fishing - starting with 48 total solved do_fishing - reducing r2c5.<249> by <2> - covered by no sets do_fishing - reducing r3c7.<247> by <2> - covered by no sets update_cell - setting r1c6 = d9 do_fishing - forcing r1c6 to d9 - covered by all sets do_fishing - reducing r4c4.<2479> by <9> - covered by no sets do_fishing - reducing r6c4.<4579> by <9> - covered by no sets do_fishing - ending with 5 updates 49 total solved do_pinnings - starting with 49 total solved update_cell - setting r1c9 = d7 update_cell - setting r2c5 = d4 update_cell - setting r3c7 = d4 update_cell - setting r4c4 = d4 update_cell - setting r6c9 = d4 update_cell - setting r8c9 = d1 update_cell - setting r9c6 = d4 update_cell - setting r9c9 = d6 do_pinnings - ending with 8 updates 57 total solved do_pinnings - starting with 57 total solved update_cell - setting r6c7 = d1 do_pinnings - ending with 1 updates 58 total solved do_pinnings - starting with 58 total solved update_cell - setting r4c7 = d6 update_cell - setting r6c2 = d6 update_cell - setting r6c8 = d9 update_cell - setting r8c7 = d9 update_cell - setting r9c7 = d7 do_pinnings - ending with 5 updates 63 total solved do_pinnings - starting with 63 total solved update_cell - setting r2c8 = d2 update_cell - setting r2c9 = d9 update_cell - setting r4c2 = d9 update_cell - setting r4c5 = d2 update_cell - setting r4c8 = d8 update_cell - setting r5c5 = d9 update_cell - setting r5c7 = d2 update_cell - setting r6c3 = d8 update_cell - setting r7c4 = d9 update_cell - setting r7c6 = d5 update_cell - setting r7c9 = d2 update_cell - setting r8c4 = d7 update_cell - setting r9c4 = d2 do_pinnings - ending with 13 updates 76 total solved do_pinnings - starting with 76 total solved update_cell - setting r3c5 = d7 update_cell - setting r3c6 = d2 update_cell - setting r4c3 = d7 update_cell - setting r6c4 = d5 update_cell - setting r6c6 = d7 do_pinnings - ending with 5 updates 81 total solved RCB solution 1 for puzzle 1 ../test/remote_triples.ss 4 8 2| 1 5 9| 3 6 7 1 7 3| 6 4 8| 5 2 9 9 5 6| 3 7 2| 4 1 8 ------+------+------ 3 9 7| 4 2 1| 6 8 5 5 4 1| 8 9 6| 2 7 3 2 6 8| 5 3 7| 1 9 4 ------+------+------ 7 1 4| 9 6 5| 8 3 2 6 2 5| 7 8 3| 9 4 1 8 3 9| 2 1 4| 7 5 6 Puzzle call statistics: do_pinnings updates/calls 53/9 5.8889 0.2883 msec 0.0320 msec/call 0.0054 msec/update do_restrictions updates/calls 0/1 0.0000 0.0151 msec 0.0151 msec/call inf msec/update do_fishing updates/calls 5/1 5.0000 1.9804 msec 1.9804 msec/call 0.3961 msec/update Puzzle 1 took 2.4584 msec for 1 solution(s) Puzzle final statistics: tot_pinnings updates/calls 53/9 5.8889 0.2883 msec 0.0320 msec/call 0.0054 msec/update tot_restrictions updates/calls 0/1 0.0000 0.0151 msec 0.0151 msec/call inf msec/update tot_fishing updates/calls 5/1 5.0000 1.9804 msec 1.9804 msec/call 0.3961 msec/update sudoku -bvg ../test/remote_triples.ss nrczt promote 0) 0 1) 0 2) 0 3) 0 4) 0 5) 0 6) 0 z_links) 0 t_links) 0 g_links) 0 nrczt search vt chains) 0 vs chains) 0 ve chains) 0 nl[0] exits) 0 nrczt 0) 0 nrczt 1) 0 nrczt 2) 0 nrczt 3) 0 nrczt 4) 0 nl exits 1) 0/0 2) 0/0 3) 0/0 4) 0/0 5) 0/0 6) 0/0 7) 0/0 8) 0/0 9) 0/0 sudoku used solving order prfdantsc -N18 -A5 -D5

3d-medusa coloring cracked it with 5 reductions.
nrczt cracked it with 2 chains and 2 bi-value cell reductions.
distributed-disjoint-subsets cracked it with 2 ADDS and 5 reductions.

Nothing exactly matched your solution of R2C5 <> 2,9 R5C7 <> 8. POM fishing was the fastest (about 2 msec) with a R2C5 <> 2. nrczt resolved R2C5 == 4 on the 2nd chain.

Removed from the nrczt group extentions topic to here

by **StrmCkr** » Sat Oct 25, 2008 6:38 pm

added a mod to the first post added in markings of x's where a pair from sub patten excludes additional 2'9s along the row...

denis -
its a combined coverset of layers 289...

. thats how i approached the pattern.

one single move.

not two.

and your way also is the same thing worded diffrent.

by **ronk** » Sat Oct 25, 2008 7:20 pm

StrmCkr wrote:its a combined coverset of layers 289...

. thats how i approached the pattern.

one single move.

not two

But there are two different "coversets."

Coverset 2r2, 9c8, 2b6, 8b6, 9r5 and 2c5 imply r2c5<>2. In chain form using NL notation ...
r2c5 -2- r2c8 -9- r46c8 -28- r5c7 -9- r5c5 -2- r2c5 ==> r2c5<>2

Coverset 9r2, 2c8, 8b6, 9b6, 2r5 and 9c5 imply r2c5<>9. In chain form ...
r2c5 -9- r2c8 -2- r46c8 -89- r5c7 -2- r5c5 -9- r2c5 ==> r2c5<>9

To consider them as one move makes no sense to me.

by **StrmCkr** » Sat Oct 25, 2008 8:32 pm

i think of it this way.

linked layers operate as a single unit.

for example
a remote pair.

if its a singular unit with coverset logic: the covering set being 2 digits.

then both end points of the code are identical the operation is a two fold restiction equal to the end point cells (2 digits). restriction in this case is line of sight to the end points. marked with x.

in the example its a
3 layer coverset with a freedom of 2 with in the layer.
where both endpoints are the same as the above. => 2 restrictions via line of sight equal to both end points.

to explain this better id have to show you how my solver works... which would not be too fun.. perhaps i should build a thread on it..

i built it using x-cell.

i broke up the standard sudoku into a
9 "planer" {layer} approach... issolating each digit to there own plane. and linking them into subplanes as pairs etc...

where subplanes fuction as 1 layer affectign both linked layers equally.

"
only thing i hate is manually entering in grids..."

any one know how to translate a 81 charter sting into 81 cells? using excel?

by **David P Bird** » Sun Oct 26, 2008 12:16 am

StrmCkr
Use the MID worksheet function to extract each character into its corresponding cell and multiply by 1 to force it to numeric.
eg
Enter 1 to 9 in A2:A10 and B1:J1 as row and column numbers
Copy the character string as text to M1
Enter "=1*MID($M$1,B$1+9*$A1,1)" in B2 and copy this to fill B2:J10

by **aran** » Mon Oct 27, 2008 4:11 am

From a hidden pair perspective :
hp89r46c8
-8r5c7 =>r5c7 <8>
-9=2r2c8 =>r2c5 <2>
-89=2r5c7-2=9r5c5 =>r2c5 <9>.

hp89r46c8=2r4c8-2=9r2c8 (=>r2c5 <9>)-9=8r6c8-8r5c7 (=>r5c7 <8>) =*9r5c7-9=2r5c5 (=>r2c5 <2>)
* combined with 2r4c8

=>r2c5 <2> <9>, r5c7 <8>

by **ronk** » Mon Oct 27, 2008 4:58 am

If this pattern deserves a name, it should at least be described (and the eliminations proven) with a generalized non-degenerate naked triple, as in the exemplar below. By that I specifically mean that all three digits can be in all three cells of the naked triple.

Code: Select all: *--------------------------------* | . . . | . . . | . . . | | . . . | . X . | . 29 . | | . . . | . . . | . . . | |----------+----------+----------| | . . . | . . . | . 289 . | | . . . | . 29 . | 289 . . | | . . . | . . . | . 289 . | |----------+----------+----------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *--------------------------------* X <> 2,9

Moreover, the term "naked triples" is not appropriate. Firstly, there is only one triple in the pattern. Secondly, the pattern behaves like a "remote naked pair", where the links between the remote pair are obviously different.

by **daj95376** » Mon Oct 27, 2008 6:42 am

ronk wrote:
Code: Select all
*--------------------------------* | . . . | . . . | . . . | | . . . | . X . | . 29 . | | . . . | . . . | . . . | |----------+----------+----------| | . . . | . . . | . 289 . | | . . . | . 29 . | 289 . . | | . . . | . . . | . 289 . | |----------+----------+----------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *--------------------------------* X <> 2,9

With the 289 Naked Triple, I can relate this pattern to a General Remote Pair through

Code: Select all: (2|9) -[r2c8]- (9|2) -[r46c8]= (9|2) =[r5c7]- (9|2) -[r5c5]- (2|9)

This is all that's needed.

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=9089&sid=9b4066ff0df80597a3b4db638fd2b66a#9089

keith wrote:Chapter 2: A More General Remote Pair

It is not necessary that the remote pair be connected by a chain of cells each having the same two candidates. Only one candidate is required.

by **Luke** » Mon Oct 27, 2008 7:42 am

StrmCkr's pattern:

Code: Select all: *-----------------------------* | . . . | . . . | . . . | | . . . | . X | . ab . | | . . . | . . . | . . . | |-------+--------+------------| | . . . | . . . | . abc . | | . . . | . ab . | ab . . | | . . . | . . . | . bc . | |-------+--------+------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *------------------------------*

X <> a because the a values form a singles chain.
X <> b because the b values form an AIC.

The puzzle reduced:

Code: Select all: *-----------------------------------------------------------* | 4 8 2 | 1 5 79 | 3 6 79 | | 1 7 3 | 6 249 8 | 5 29 249 | | 9 5 6 | 3 247 247 | 247 1 8 | |-------------------+-------------------+-------------------| | 3 69 78 | 2479 2479 1 | 46 289 5 | | 5 4 1 | 8 29 6 | 29 7 3 | | 2 69 78 | 4579 3 4579 | 146 89 146 | |-------------------+-------------------+-------------------| | 7 1 4 | 259 6 259 | 8 3 29 | | 6 2 5 | 79 8 3 | 179 4 179 | | 8 3 9 | 247 1 247 | 267 5 267 | *-----------------------------------------------------------*

a = 2, singles chain: [r2c8]=[r4c8]=[r5c7]=[r5c5], [r2c5]<>2
b = 9, AIC: 9[r2c5]-9[r2c8]=2[r2c8]-2[r4c8]=2[r5c7]-2[r5c5]=9[r5c5]-9[r2c5], [r2c5]<>9.

by **udosuk** » Mon Oct 27, 2008 7:49 am

daj95376 wrote:
ronk wrote:
Code: Select all
*--------------------------------* | . . . | . . . | . . . | | . . . | . X . | . 29 . | | . . . | . . . | . . . | |----------+----------+----------| | . . . | . . . | . 289 . | | . . . | . 29 . | 289 . . | | . . . | . . . | . 289 . | |----------+----------+----------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *--------------------------------* X <> 2,9

With the 289 Naked Triple, I can relate this pattern to a General Remote Pair

Perhaps Remote Pair with Grouped Strong Link is more descriptive.

The main point here is not the triple. It's the grouped strong link of 2 (& 9) in r46c8+r5c7 that allows the remote pair to work. For example you can even make it a quad or a quint:

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.)

In JSudoku this move will be detected as 2 separated "Grouped Y-wings" (i.e. W-wings) of 2 & 9 respectively. :idea:

by **ronk** » Mon Oct 27, 2008 8:23 am

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 :?:

by **PIsaacson** » Mon Oct 27, 2008 9:25 am

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

Can this be analyzed as an example of subset counting?

Multiplicities for candidates 2/8/9 = 2/1/2 total 5 for 5 cells.
r2c5 = 2 reduces total multiplicity to 4 - illegal?
r2c5 = 9 reduces total multiplicity to 4 - illegal?

by **StrmCkr** » Mon Oct 27, 2008 11:06 am

wow.. lots of attention.

thanks guys i was trying to extend the pattern into quads and quintouples today with not much luck..

other thoughts are back into UR forms?

and yes paul it can..

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