Revealing twins

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Revealing twins

Postby dyitto » Mon Jan 10, 2011 11:30 pm

First some terminology:

Suppose we have two completed grids.
Suppose that for a certain digit k, when we look at all positions of k within the first grid, the same positions in the second grid contain 1-9 uniquely.
Then one could say that digit k of the first grid reveals a group in the second grid.

Two grids with similar relationships could then be called revealing twins.

I've created two puzzles based on the following revealing digits:
1 in the first grid reveals a group in the second grid
9 in the second grid reveals a group in the first grid

Example of how to apply these constraints:

Code: Select all
1..|...|...     2..|...|...
...|...|7..     ...|...|9..
...|...|...     ...|...|...
---+---+---     ---+---+---
.1.|...|...     .?.|...|...
...|...|...     ...|...|...
...|...|...     ...|...|...
---+---+---     ---+---+---
..?|...|...     ..9|...|...
...|...|...     ...|...|...
...|...|...     ...|...|...


In the second grid R4C2 <> 2. In the first grid R7C3 <> 7.

Revealing twin 1:

Image

http://www.scrybqj.com/images_diversen/ ... ns_no1.pdf

Code lines:
Code: Select all
000309600008000000070462050309048010005000000000000030000000000000800009902010000
080000000005970000047000002700604000003000000600090100064007028000003704000000003


Revealing twin 2:

Image

http://www.scrybqj.com/images_diversen/ ... ns_no2.pdf

Code lines:
Code: Select all
010000007298001000000960000003006000000000082001008600000209014300000700000080000
003900000090458007000000040280000000071080400000000500000000060000100203008020001


These puzzles should be solvable with singles, pairs, triples, ... and also locked candidates and pointing pairs.

I'm still looking for an example grid with two revealing dgits in both directions (or the computer will while I'm asleep).
Last edited by dyitto on Sun Aug 12, 2012 8:42 am, edited 2 times in total.
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Re: Revealing twins

Postby BryanL » Tue Jan 11, 2011 11:05 am

It took a while because i kept making mistakes...

A lot of backwards and forwards between each puzzle - as one would expect.

There was a swordfish at one point in puzzle 1 but i think if i had moved to puzzle 2 that would have killed the swordfish.

Code: Select all
254|389|671
698|157|342
173|462|958
-----------
369|248|517
485|731|296
721|596|834
-----------
817|925|463
536|874|129
942|613|785


986|421|375
235|978|461
147|536|892
-----------
751|684|239
493|712|586
628|395|147
-----------
364|157|928
819|263|754
572|849|613
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Re: Revealing twins

Postby BryanL » Tue Jan 11, 2011 12:05 pm

For the second pair, there was an x-wing in puzzle 1.

Eventually i had to trial and error the 3,5 in r7c7 - probably missed something...

Code: Select all
516|832|947
298|471|536
734|965|821
-----------
483|726|159
675|193|482
921|548|673
-----------
867|259|314
352|614|798
149|387|265

423|967|815
196|458|327
857|312|649
-----------
285|743|196
971|586|432
634|291|578
-----------
712|835|964
569|174|283
348|629|751
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Re: Revealing twins

Postby dyitto » Tue Jan 11, 2011 9:27 pm

Hi BryanL, thanks for the solutions! They match mine.
For me tricky pointing pairs with the revealed groups did the trick - which is what I know my solver does.
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Re: Revealing twins

Postby BryanL » Wed Jan 12, 2011 9:21 am

dyitto wrote:For me tricky pointing pairs with the revealed groups did the trick - which is what I know my solver does.

Hi dyitto,

I looked up pointing pairs - a rather ambiguous term as there could be 3 in a mini row/col - and it is locked candidates type 1.

Below is where i got to before i used t/e. The asterisks show the group defined by the 9 in puzzle 2, leaving 3457 to be set in r4c8, r6c5, r7c7 and r9c6. I don't see any locked candidates... I guess there is a forcing chain there using the group...

Code: Select all
45    1    6    | 8*    345   2345  | 9    2345  7 
2     9*   8    | 3457  3457  1     | 345  3456  356
457   3    457  | 9     6     245   | 8    245   1*
----------------------------------------------------
4579  8    3    | 457   2     6     | 1    457*  59
6*    57   45   | 1     9     3457  | 345  8     2 
4579  2    1    | 3457  3457* 8     | 6    3457  359
----------------------------------------------------
8     6    57   | 2     357   9     | 35*  1     4 
3     45   2*   | 6     1     45    | 7    9     8 
1     457  9    | 345   8     3457* | 2    356   356


Looking at it again

If r7c7 = 3 or 5, r9c6 = 7.

If r7c7 = 5, both r4c8 and r6c5 can only be 4 so r7c7 = 3.

Did you see something simpler?

Edit: Never looked hard enough... r7c5 can never be 3, which i guess is your pointing?
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Re: Revealing twins

Postby dyitto » Wed Jan 12, 2011 9:36 pm

In your last grid:

Indeed R7C5 can see all options that are left for 3 in the revealed group.
So R7C5 can't be 3.

Also 7 in box 8 can go in R7C5 or in R9C6.
R6C5 sees both of them so R6C5 can't be 7.

That's how I understand pointing pair.
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Re: Revealing twins

Postby dyitto » Thu Jan 13, 2011 6:42 am

dyitto wrote:I'm still looking for an example grid with two revealing dgits in both directions (or the computer will while I'm asleep).

1 & 2 in the first grid reveal a group in the second grid
8 & 9 in the second grid reveal a group in the first grid

Image

http://www.scrybqj.com/images_diversen/ ... _12_89.pdf

Code lines:
Code: Select all
002000000000900000003510070020000000060100000000000200400000560006004000000000000
090000000012500800000000000005000240073000010000030500000403000940080020020050006
Last edited by dyitto on Sun Aug 12, 2012 8:43 am, edited 1 time in total.
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Re: Revealing twins

Postby BryanL » Thu Jan 13, 2011 7:10 am

Hi dyitto,

thanks for the continuing puzzles - they are nice challenge.

May I suggest posting in the following format instead of graphics.

Code: Select all
..2|...|...
...|9..|...
..3|51.|.7.
-----------
.2.|...|...
.6.|1..|...
...|...|2..
-----------
4..|...|56.
..6|..4|...
...|...|...

.9.|...|...
.12|5..|8..
...|...|...
-----------
..5|...|24.
.73|...|.1.
...|.3.|5..
-----------
...|4.3|...
94.|.8.|.2.
.2.|.5.|..6


Here is a link to http://forum.enjoysudoku.com/new-topics-how-to-ask-for-help-t2664.html a forum post about posting guidelines.

Just makes it easier to copy and paste.

Thx again for the puzzles,

Bryan
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Re: Revealing twins

Postby dyitto » Fri Jan 14, 2011 6:29 am

It's now relatively easy to create puzzles of the first type. I could put some more puzzles online somewhere if appreciated.
It takes lots of time for the computer to find grids for more complicated variants.

Code: Select all
5..|4..|6..
..2|1..|...
...|.8.|...
---+---+---
37.|...|.9.
..6|.7.|...
.21|.5.|8..
---+---+---
.9.|...|2..
...|9.4|...
...|...|...


.62|..4|..5
...|27.|...
.4.|1..|9..
---+---+---
...|..1|...
9..|...|...
...|..9|5.3
---+---+---
...|...|7..
..1|...|.2.
.8.|.3.|6..


...|..5|..1
...|8.3|...
.53|.6.|...
---+---+---
4.2|...|...
8..|...|29.
...|9..|68.
---+---+---
.31|.8.|...
...|7..|...
9..|.5.|.2.


1 in grid 1 reveals a group in grid 2
2 in grid 2 reveals a group in grid 3
3 in grid 3 reveals a group in grid 1


Two grids with 3 revealing digits each direction haven't been found yet after running for 8 hrs.
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Re: Revealing twins

Postby BryanL » Sat Jan 15, 2011 4:20 am

Code: Select all
589|423|617   362|894|175   784|295|361
762|195|438   819|275|436   169|843|752
143|786|952   547|163|982   253|167|849
-----------   -----------   -----------
378|642|591   673|521|849   492|678|513
956|871|324   958|346|217   876|531|294
421|359|876   124|789|563   315|924|687
-----------   -----------   -----------
894|517|263   236|918|754   531|482|976
237|964|185   491|657|328   628|719|435
615|238|749   785|432|691   947|356|128

589423617762195438143786952378642591956871324421359876894517263237964185615238749
362894175819275436547163982673521849958346217124789563236918754491657328785432691
784295361169843752253167849492678513876531294315924687531482976628719435947356128

Didn't get the one before with two numbers in each twin but didn't give it any time...
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Re: Revealing twins

Postby BryanL » Sun Jan 16, 2011 10:15 am

dyitto wrote:1 & 2 in the first grid reveal a group in the second grid
8 & 9 in the second grid reveal a group in the first grid

Code: Select all
002000000000900000003510070020000000060100000000000200400000560006004000000000000
090000000012500800000000000005000240073000010000030500000403000940080020020050006


that was tough...

Code: Select all
172|648|395
685|937|124
943|512|678
-----------
729|456|813
864|123|957
531|789|246
-----------
498|371|562
256|894|731
317|265|489


798|364|152
612|597|834
534|812|679
-----------
165|978|243
273|645|918
489|231|567
-----------
856|423|791
947|186|325
321|759|486

172648395685937124943512678729456813864123957531789246498371562256894731317265489

798364152612597834534812679165978243273645918489231567856423791947186325321759486
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Re: Revealing twins

Postby dyitto » Sun Jan 16, 2011 8:37 pm

Your solutions all match mine.
Yeah it's tough, however it's the stadium of making mistakes with a constraint we're not yet used to.
It would be nice if we could exploit some very specific solving techniques.

Considering opposites as a special case of these revealed groups, RW has given some excellent ideas.
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Re: Revealing twins

Postby dyitto » Wed Jan 19, 2011 11:32 pm

dyitto wrote:Two grids with 3 revealing digits each direction haven't been found yet after running for 8 hrs.

Aargh
New depth-first algorithm with recursion: Out of memory after running for 3 seconds :cry:
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Re: Revealing twins

Postby BryanL » Thu Jan 20, 2011 5:43 am

dyitto wrote:It's now relatively easy to create puzzles of the first type. I could put some more puzzles online somewhere if appreciated.


I would have thought here was fine... ;)
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Re: Revealing twins

Postby BryanL » Thu Jan 20, 2011 5:46 am

dyitto wrote:Aargh
New depth-first algorithm with recursion: Out of memory after running for 3 seconds :cry:


How are you searching for them?

Just start with a random puzzle and try and create another from it? Some other way???

I may try and create a few...
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