The New Sudoku Players' Forum

[dyitto]

Killer sudoku with Opposites of 1 constraint:

[Pyrrho]

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

Pyrrhon

[dyitto]

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.

[HATMAN]

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

[dyitto]

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.

[HATMAN]

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

[dyitto]

I've taken another grid:

Code: Select all

9|5|6|7|2|3|1|4|8
2|8|3|1|4|9|5|6|7
4|1|7|5|8|6|2|3|9
5|9|2|3|6|1|8|7|4
3|4|8|9|7|2|6|1|5
7|6|1|8|5|4|9|2|3
6|2|5|4|9|7|3|8|1
1|7|9|6|3|8|4|5|2
8|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|.|.|4
3|4|.|.|.|2|.|1|5
.|.|1|.|5|4|.|2|3
.|2|5|4|.|.|3|.|1
1|.|.|.|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.

[dyitto]

Code: Select all

123456789
984372615
657189432
716298354
532741968
849635127
275963841
468517293
391824576


[HATMAN]

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.