Luke451 wrote:Thanks, Don. The latter two seem so obvious now, but I was side-tracked into the notion that somehow they related to some variation like als-xz. Now I’ll have to delve into what “sis” is all about.

I’d like to say I appreciate how patient and indulgent the SPF cadre is when helping folks like me catch up on topics in which they've long been conversant. I know it must make their eyes roll sometimes. Hopefully there are other intermediate players who got something out of this as well. I know this, though: in the last three days I’ve solved two of the puzzles in my “stuck pile” as a result of this. Very happy!

For info :

sis is a simple notion with interesting possibilities.

It just means that one candidate in a set (whatever the size) must be true.

A bivalue or or a bilocal is the elementary case.

If there are 3 6's in a column say 6r127c1 then {6r1c1, 6r2c1, 6r7c1} is an sis : one of those is true.

Use of sis ultimately amounts to finding a conclusion either elimination or placement on which all members of the set agree.

To that extent, there is elegant and less elegant use of the idea. Enter subjectivity...

Eg if r1c1 has three candidates 148 then {1,4,8} is an sis. To go looking for a conclusion on which all agree might not/would probably not be "elegant".

A nice idea in this field is Transport developed I think by Re'born (but not sure).

In summary :

let{a,b,c} be an sis

Suppose aTrue=>ATrue, bTrue=>BTrue, cTrue=>CTrue

then {A,B,C} is also an sis (easily proved).

As are {a, B, C} {a, b, C} and so on.

So you can improve the original sis, by transporting one or several or all of the members and then work with the new improved version !