re'born wrote:Denis,

When you wrote your new version of SudoRules, all of the (h)xy(z)(t)-chains went away, and were replaced by nrc(z)(t)-chains (at least in the solutions I've seen). Of course, xyt, xyzt and hxy-chans are all subsumed by nrczt-chains (as I think you mentioned earlier), but what happens to hxyt and hxyzt chains? It seems that these should still be giving you something extra. Do you have any such examples? Are hxy(z)(t)-chains still implemented in SudoRules? And have you tried going one step further and implementing hnrc(z)(t)-chains?

SudoRules 13 is an extension of SudoRules 12. All that was in version 12 is totally unchanged. In version 13, only 3D chains (nrc-, nrct-, nrczt-) have been added.

For any puzzle, there are lots of possible solution paths.

SudoRules choices rely on the priorities ascribed to the rules.

2D chains are chains of cells in 2D spaces (rc-, rn-, cn-). All their links are in the same 2D space.

3D chains are chains of cells in 3D-space (nrc-space), i.e. chains of candidates.Their links are in 3D space, they are more complex.

When the two types of chains are mixed, some penalty should be put on the 3D chains wrt the 2D chains of the same length (unless one considers that spotting a bivalue is as easy as spotting conjugate candidates).

This penalty is a parameter in SudoRules. In all the examples I've given, it was set to 0, in order to illustrate the new rules. But, if you change the penalty, 2D rules will be applied more often. On the contrary, if you put a very high penalty, 3D rules will appear very rarely.

With penalty 0, as there are more possibilities with 3D chains than with 2D, 3D chains appear more often than 3D. But 2D chains also appear sometimes.