Calcudoku puzzle forumhttp://www.calcudoku.org/forum/ A non-unique and yet unique solutionhttp://www.calcudoku.org/forum/viewtopic.php?f=16&t=98 Page 2 of 2

 Author: arjen  [ Sun Nov 06, 2011 9:01 am ] Post subject: Re: A non-unique and yet unique solution You can use the [ code ] tag for  Code: Although its not possible for 1 space.  But it is for 2.   Or 3,

 Author: giulio  [ Sun Nov 06, 2011 12:44 pm ] Post subject: Re: A non-unique and yet unique solution Thanks. I thought that the Code tags would keep the indentations, but I felt it wasn't code. When one is a purist...

 Author: giulio  [ Mon Nov 07, 2011 3:16 am ] Post subject: Re: A non-unique and yet unique solution Patrick suggested that I post a snapshot of the 12x12 puzzle that started this thread once the solution was published. Here it is:I have highlighted the four cells that make the grid non-unique, although the CalcuDoku still has a unique solution.

 Author: pnm  [ Mon Nov 07, 2011 11:30 am ] Post subject: 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 definean operation as you described:- for 2 distinct cells in the grid, consider the 4 corner cells determined by those 2, and rotate once clockwiseThen 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 ... 2which 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 gridsuch that you will still call it a non-unique grid).Patrick

 Author: giulio  [ Mon Nov 07, 2011 1:01 pm ] Post subject: Re: A non-unique and yet unique solution When I saw two pairs of digits that I could swap without violating the rules of unicity of rows and columns, I found it very surprising. Especially because I had stumbled on them by chance. But it is in fact a fairly common occurrence. Just by looking at the puzzle, I found two other pairs that behave in exactly the same way: b3/c3 and b4/c4. Then, I looked at one of my puzzles and, within less than a minute, I spotted the same configuration.As you say, one can also imagine a whole series of increasingly complex swaps that would keep the unicity rules satisfied. A simple 'square' swap is just easier to spot. I agree that without a definition of unicity, such a statement is meaningless.My apologies for saying that your puzzle had a non-unique grid. It sounded bad. At least, my post gave us the opportunity to talk about other things...

 Author: pnm  [ Mon Nov 07, 2011 1:05 pm ] Post subject: Re: A non-unique and yet unique solution giulio wrote:My apologies for saying that your puzzle had a non-unique grid. It sounded bad. At least, my post gave us the opportunity to talk about other things... No, exactly, don't worry about it.(catchy headlines to increase readership )I'd probably only define two grids to be identical if they can be transformedinto one another by rotation or mirroring (of the whole grid).(I think using the word "unique" is confusing here)Patrick

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