On Sun, Jun 19, 2022 at 12:42 PM Brian Schott <schott.br...@gmail.com> wrote:
> Instead I want to look more closely at his results for the verbs
> AR and AC. In his algorithm he takes the larger of the two results, that is
> the larger of AR or AC , where he expects one of each pair to be zero and
> the other to be a valid candidate. Whenever there is a nonzero AC it is a
> unique and correct candidate, but the values for AR are selected using
> index of, i. . I am suspicious that the selection of AR is almost arbitrary
> and is causing the problem. I think a human being could do a better job of
> selecting among the alternatives from AR.

My understanding is that ar and ac are approaching the solution "from
the opposite ends".

ac looks for *positions* which are completely constrained -- these
positions have only one possible value

ar looks for *values* which are completely constrained -- these values
have only one possible position. So I guess my concern could have been
rephrased as: what happens when ar tries to assign values when the
positions are not completely constrained?

> If I am correct about using AR and AC to help a human, I would use a
> variation on AC that shows all of the possible results instead of the one
> captured by the ‘index of’ primitive. In light of that I am looking for
> ways to use 4 x 4 arrangements of dots to display each of the cell’s
> information. I was looking in the Unicode lists for 4 x 4 dot arrangements
> but was unable to find any, so I am trying to imagine alternatives. So far
> I can only think of using viewmat to construct the dot patterns.

If viewmat is acceptable, and you are using jqt, you might want to
consider using wd to present the grid.

That said, a 4 4 $ of some ascii characters might also work. (But a wd
based approach would allow you to "highlight" or emphasize the
corresponding row and column also.)

That said, if you do not address the underlying lack of complete
constraint in the puzzle design, this might turn out to be quite a bit
more difficult than sudoku. (Do you have worked examples illustrating
this puzzle variation? If so, maybe the difficulty is a feature rather
than a bug...)

I hope this helps,

-- 
Raul
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