Re: A non-unique and yet unique solution
giulio wrote:
I have highlighted the four cells that make the grid non-unique, although the CalcuDoku still has a unique solution.
It depends on how you define a non-unique grid. In this case you could first define
an operation as you described:
- for 2 distinct cells in the grid, consider the 4 corner cells determined by those 2, and rotate once clockwise
Then define two grids to be equivalent if one such operation results in the same grid.
(what you call "non-unique").
That said, you can apply this operation more than once. Does this make the resulting grid "non-unique"?
And what about larger operations like this? For example, you could find this arrangement in a grid:
Code:
4 ... 2 ... 1
. . .
2 ... 1 ... 4
. . .
1 ... 4 ... 2
which you can rotate as well. Does this mean this grid is "non-unique"?
(in general, what set of permutations are you allowed to apply to the grid
such that you will still call it a non-unique grid).
Patrick