## Revealing twins

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Revealing twins

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:

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

Code lines:
Code: Select all
`000309600008000000070462050309048010005000000000000030000000000000800009902010000080000000005970000047000002700604000003000000600090100064007028000003704000000003`

Revealing twin 2:

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

Code lines:
Code: Select all
`010000007298001000000960000003006000000000082001008600000209014300000700000080000003900000090458007000000040280000000071080400000000500000000060000100203008020001`

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.
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Revealing twins

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|671698|157|342173|462|958-----------369|248|517485|731|296721|596|834-----------817|925|463536|874|129942|613|785986|421|375235|978|461147|536|892-----------751|684|239493|712|586628|395|147-----------364|157|928819|263|754572|849|613`
BryanL

Posts: 247
Joined: 28 September 2010

### Re: Revealing twins

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|947298|471|536734|965|821-----------483|726|159675|193|482921|548|673-----------867|259|314352|614|798149|387|265423|967|815196|458|327857|312|649-----------285|743|196971|586|432634|291|578-----------712|835|964569|174|283348|629|751`
BryanL

Posts: 247
Joined: 28 September 2010

### Re: Revealing twins

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.
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Revealing twins

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  356457   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?
BryanL

Posts: 247
Joined: 28 September 2010

### Re: Revealing twins

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.
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Revealing twins

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

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

Code lines:
Code: Select all
`002000000000900000003510070020000000060100000000000200400000560006004000000000000090000000012500800000000000005000240073000010000030500000403000940080020020050006`
Last edited by dyitto on Sun Aug 12, 2012 8:43 am, edited 1 time in total.
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Revealing twins

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
BryanL

Posts: 247
Joined: 28 September 2010

### Re: Revealing twins

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 22 in grid 2 reveals a group in grid 33 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.
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Revealing twins

Code: Select all
`589|423|617   362|894|175   784|295|361762|195|438   819|275|436   169|843|752143|786|952   547|163|982   253|167|849-----------   -----------   -----------378|642|591   673|521|849   492|678|513956|871|324   958|346|217   876|531|294421|359|876   124|789|563   315|924|687-----------   -----------   -----------894|517|263   236|918|754   531|482|976237|964|185   491|657|328   628|719|435615|238|749   785|432|691   947|356|128589423617762195438143786952378642591956871324421359876894517263237964185615238749362894175819275436547163982673521849958346217124789563236918754491657328785432691784295361169843752253167849492678513876531294315924687531482976628719435947356128`

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

Posts: 247
Joined: 28 September 2010

### Re: Revealing twins

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
`002000000000900000003510070020000000060100000000000200400000560006004000000000000090000000012500800000000000005000240073000010000030500000403000940080020020050006`

that was tough...

Code: Select all
`172|648|395685|937|124943|512|678-----------729|456|813864|123|957531|789|246-----------498|371|562256|894|731317|265|489798|364|152612|597|834534|812|679-----------165|978|243273|645|918489|231|567-----------856|423|791947|186|325321|759|486172648395685937124943512678729456813864123957531789246498371562256894731317265489798364152612597834534812679165978243273645918489231567856423791947186325321759486`
BryanL

Posts: 247
Joined: 28 September 2010

### Re: Revealing twins

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.
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Revealing twins

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
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Revealing twins

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...
BryanL

Posts: 247
Joined: 28 September 2010

### Re: Revealing twins

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

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...
BryanL

Posts: 247
Joined: 28 September 2010

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