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

14 posts
• Page **1** of **1**

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

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

Many thanks

www.brightonandhove.org

- stuartn
**Posts:**211**Joined:**18 June 2005

stuartn wrote: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.

- Nick70
**Posts:**156**Joined:**16 June 2005

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...

...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...

- Karyobin
**Posts:**396**Joined:**18 June 2005

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:

B) Two weakly linked cells:

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

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:

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 :

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

or

E) What about:

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

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

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

A) These are two strongly linked cells:

- Code: Select all
`[12][12]`

B) Two weakly linked cells:

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`[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?

- tso
**Posts:**798**Joined:**22 June 2005

tso wrote: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.

- angusj
**Posts:**306**Joined:**12 June 2005

Ok, I'm still confused.

... have a conjugate relationship.

... do not have a conjugate relationship.

... ?

- 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]`

... ?

- tso
**Posts:**798**Joined:**22 June 2005

tso wrote:

- 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.

- angusj
**Posts:**306**Joined:**12 June 2005

tso wrote:

- 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".

- Nick70
**Posts:**156**Joined:**16 June 2005

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