SpAce wrote:denis_berthier wrote:If 69 candidates out of 146 lead to a contradiction, then the manual solver has a high chance of finding one by starting from anywhere. He has still a much larger chance if he starts from a partial-whip[1].

Why? This is the part I don't understand. The possible targets are still fixed and very limited

They are obviously more limited with the partial-whip[1] condition than with no condition at all. Thus, the manual user has fewer chances of trying a candidate that leads nowhere.

SpAce wrote:except with t-whips that allow growing the chain both ways. I don't see how that possibility depends on starting with a partial-whip[1].

In order to build a t-whip[n], you must already have a partial-whip[n-1] (A full t-whip[1] is a whip[1].)

SpAce wrote:Do you always start looking for whips with a partial-whip[1]?

Yes.

SpAce wrote:What about whips that start with a bivalue cell?

It's not a problem. It's just the particular case when the first partial-whip[1] has no t-candidate.

SpAce wrote:Or do you count bivalue cells as partial-whips[1], too?

I now guess you mean rc-bivalue. First, not the bivalue cell itself; the target z must also be specified. But, with these conditions, yes, of course, they also make partial-whips[1].

SpAce wrote:but extremely confusing, considering that you always tell that whip[1] means intersections

I don't say that a whip[1] is an intersection in the sense that it'd be the mathematical intersection of a row (or columnn) and a block. It is an intersection in terms of a resolution rule, including a target.

What may confuse you is, you have to realise that there is no whip[1] consisting of a target plus an rc-bivalue cell. But that may make a partial-whip[1].

More generally, it's interesting to notice that, in any CSP, one may have whips[2 or more] without having whips[1] - said otherwise, no whips[1] but partial-whips[1]. This is the case in Latin Squares. In such CSPs, there are no g-whips.SpAce wrote:(*) Logically a naked single should be a whip[1]

Logically, there'd be no difference between Naked or Hidden Singles.

Singles are not included in the definition of whips. The definition requires a precise pattern.