The New Sudoku Players' Forum

[stuartn]

Could our sagacious friends provide a readable explanation of the difference betwen a 'strong' and 'weak' leak in a forcing chain please?

The recent postings aren't quite 'graspable' for some.

Many thanks

www.brightonandhove.org

[Karyobin]

You are the weak link.

Hurrr hurrr.

[gadgetman]

Shouldn't that be 'you are the weakest link'?

And shouldn't you have an awful hairdo and look like you've just eaten a lemon when you say that?

[stuartn]

The Stella pixie aside chaps - I was quite serious.....

[Nick70]

Could our sagacious friends provide a readable explanation of the difference betwen a 'strong' and 'weak' leak in a forcing chain please?

A weak link is a relationship between two possibilities that exclude each other: for example number 4 can be in r1c4 or in r1c7 (or in neither of them), but it cannot be in both.

A strong link is a relationship between two possibilities one of which must be true and the other false. For example a cell that can contain 5 or 7, and no other number.

[Karyobin]

Quality stuff again, Nick70. An' I'll have you know, Stuarty-baby, that I posted that before I had a drink tonight. I've just finished calling the quiz now however, an' they feed me Stella all night till I stop...

...Oooohh, the playful *fizz* on your tongue...

...anyway, earlier on - that was just Stella-anticipation talking. Not the real thing.

That's now.

God, I need this Chinese food...

[stuartn]

Thanks chaps..... Nick70 - your clarity is clearly unbefuddled by Stella or Gin (or a couple of tinnies on the train home). Marvellous.

[tso]

I thought I understood how the terms strong and weak links were used, but now I'm confused. Where I'm I right and wrong here? I'm not trying to understand the logic, just the common usage.

A) These are two strongly linked cells:

Code: Select all

[12][12]

B) Two weakly linked cells:

Code: Select all

[12][13]

C) Ok -- I think that's right. But what about:

Code: Select all

[123][145]

or

[123][123]


Are these considered weakly linked (Always? Just in some contexts? Never?) because of the shared candidates? Are *any* two cells with at least one shared candidate considered to have a weak link?

D) What about this triplet:

Code: Select all

[12][23][13]

Is this considered 3 cells with weak links to the other 2, or 3 stongly linked cells? The group of 3 cells, taken together, have exactly two states -- in this case, 1-2-3 or 2-3-1 -- just as it would be if it were three stongly linked cells such as this :

Code: Select all

[12][12]
[12]


... which have, as a group, only two states ...

Code: Select all

[2][1]
[1]


or

Code: Select all

[1][2]
[2]


E) What about:

Code: Select all

[123][123][123]

Is this just three weakly linked cells, as there are 6 possible states?

F) How would these three sets of four cells be charactorized?

Code: Select all

[12][13][14][15]

and

[12][23][34][45]

and

[12][23][34][15]


How are weak/strong links related to or contrasted with conjugates?

[angusj]

How are weak/strong links related to or contrasted with conjugates?

I think a "strong" link is generally used to describe conjugate relationships - where if a is true then b is false and conversly if a is false then b is true. I would define a "weak" link as non-conjugate relationship where if a is true then b is false but if a is false then b remains undefined.

I now try to avoid using the terms "strong" and "weak" since they may have different meanings to others.

[tso]

Ok, I'm still confused.

Code: Select all

[12][12]

... have a conjugate relationship.

Code: Select all

[12][13]

... do not have a conjugate relationship.

Code: Select all

[12][23][13]

... ?

[angusj]

Code: Select all

[12][23][13]

... ?

I would argue that each cell has a conjugate relationship with each other since assigning any one cell implicitly assigns all of them. However, I can equally accept that since this isn't strictly a binary true/false relationship it isn't "conjugate". So, having an each way bet ... I guess this is where it's better to describe a relationship rather than give it a confusing label.

[Nick70]

Code: Select all

[12][23][13]

... ?

The links are between candidates, not between cells.

Let's call the three cells A, B and C.

There's a a strong link between A=1 and A=2. If one is false then the other is true.

There's a strong link between A=2 and B=2. If one is false than the other is true.

And so on.

So when you have a weak link you say: "if I promote this candidate to big number, then I can remove this other candidate".

When you have a strong link you say: "if I remove this candidate, then I can promote this other candidate to big number".

[angusj]

The links are between candidates, not between cells.

Well put, and well explained too.

[tso]

Got it. Thanks!