Killer with opposites of 1

For fans of Killer Sudoku, Samurai Sudoku and other variants

Killer with opposites of 1

Killer sudoku with Opposites of 1 constraint:

Last edited by dyitto on Sun Aug 12, 2012 9:07 am, edited 1 time in total.
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dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

Re: Killer with opposites of 1

The opposite of 1 variants remember me to the old variant where the opposites must sum up to 10.

Pyrrhon
Pyrrho

Posts: 3
Joined: 10 December 2010

Re: Killer with opposites of 1

Pyrrho wrote:The opposite of 1 variants remember me to the old variant where the opposites must sum up to 10.

Pyrrhon

Perhaps a mix between Opposites of 1 and Twin Equivalent could be possible:
Two grids.
Each digit 1-9 in the solution to one grid reveals a constraint group in the other grid - and vice versa.
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dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

Re: Killer with opposites of 1

That feels like an extremely tight constraint - need to check is it is possible on a latin square first.
HATMAN

Posts: 264
Joined: 25 February 2006
Location: Nigeria

Re: Killer with opposites of 1

Well I tried 7 random Classical sudoku grids.
All of them 0 solutions - should the digits have indicated the extra constraint groups in another grid.

Let alone the vice versa part.
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dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

Re: Killer with opposites of 1

This Latin Square Twins with the set of top left to bottom right diagonals

198765432
321987654
543219876
765432198
987654321
219876543
432198765
654321987
876543219

Just played around a little but I think this is impossible for a sudoku. A start on 123 might be like this:
| 1 X X | 2 X X | 3 X X |
| X 3 X | X 1 X | X 2 X |
| X X 2 | X X 3 | X X 1 |
--------------------------------------
| 3 X X | 1 X X | 2 X X |
| X 2 X | X 3 X | X 1 X |
| X X 1 | X X 2 | X X 3 |
-------------------------------------
| 2 X X | 3 X X | 1 X X |
| X 1 X | X 2 X | X 3 X |
| X X 3 | X X 1 | X X 2 |
which gives:
| 1 X X | 9 X X | 2 X X |
| X 3 X | X 2 X | X 1 X |
| X X 2 | X X 4 | X X 3 |
-------------------------------------
| 5 X X | 4 X X | 3 X X |
| X 4 X | X 6 X | X 5 X |
| X X 6 | X X 5 | X X 7 |
-------------------------------------
| 6 X X | 8 X X | 7 X X |
| X 8 X | X 7 X | X 9 X |
| X X 1 | X X 9 | X X 8 |
But I cannot see a useful way of going on
HATMAN

Posts: 264
Joined: 25 February 2006
Location: Nigeria

Re: Killer with opposites of 1

I've taken another grid:

Code: Select all
`9|5|6|7|2|3|1|4|82|8|3|1|4|9|5|6|74|1|7|5|8|6|2|3|95|9|2|3|6|1|8|7|43|4|8|9|7|2|6|1|57|6|1|8|5|4|9|2|36|2|5|4|9|7|3|8|11|7|9|6|3|8|4|5|28|3|4|2|1|5|7|9|6`

and I've taken digits 1-5:

Code: Select all
`.|5|.|.|2|3|1|4|.2|.|3|1|4|.|5|.|.4|1|.|5|.|.|2|3|.5|.|2|3|.|1|.|.|43|4|.|.|.|2|.|1|5.|.|1|.|5|4|.|2|3.|2|5|4|.|.|3|.|11|.|.|.|3|.|4|5|2.|3|4|2|1|5|.|.|.`

It tuns out that if these digits are indicating constraints in another grid,
then this other grid is already uniquely defined apart from permuting the digits 1-9.

In other words:

Code: Select all
`1|2|3|4|5|6|7|8|9.|.|.|.|.|.|.|.|..|.|.|.|.|.|.|.|..|.|.|.|.|.|.|.|..|.|.|.|.|.|.|.|..|.|.|.|.|.|.|.|..|.|.|.|.|.|.|.|..|.|.|.|.|.|.|.|..|.|.|.|.|.|.|.|.`

has one solution.

Maybe tomorrow I'll have the one solution.
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

Re: Killer with opposites of 1

Code: Select all
`123456789984372615657189432716298354532741968849635127275963841468517293391824576`
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

Re: Killer with opposites of 1

1 to 5 are good but it fails on 678 and 9

I had expected the solutions to be two-way twins (as per the latin square) - but that does not have to be the case - so maybe it is possible.
HATMAN

Posts: 264
Joined: 25 February 2006
Location: Nigeria