The New Sudoku Players' Forum

[daj95376]

Here, a strong link represents a Conjugate Pair:

(9) [r4c5]=[r4c9]

Here, a weak link extends the expression by one cell:

(9) [r4c5]=[r4c9]-[r9c9]

Is there a term to declare [r4c5] and [r9c9] either true or false, together, for (9)?

If not, is there any objection to my calling them Equivalent Pair?

[Edit: Changed title and improved readibility of links.]

BTW: My apologies if I asked this question in the past and forgot the answer!

[ravel]

Is there a term to declare [r4c5] and [r9c9] either true or false, together?

[r4c5]=[r4c9]=[r9c9] ?

If not, is there any objection to my calling them Equivalent Candidates?

For me its fine

[daj95376]

Sorry ravel for the abbreviated information in the links. I've updated my initial post ... and changed Candidates to Pair in the title and text. Hopefully, it makes more sense now.

[re'born]

Here, a strong link represents a Conjugate Pair:

(9) [r4c5]=[r4c9]

Here, a weak link extends the expression by one cell:

(9) [r4c5]=[r4c9]-[r9c9]

Is there a term to declare [r4c5] and [r9c9] either true or false, together, for (9)?

If not, is there any objection to my calling them Equivalent Pair?

[Edit: Changed title and improved readibility of links.]

BTW: My apologies if I asked this question in the past and forgot the answer!

I don't see how in your expression you obtain r4c5=9 => r9c9 = 9. If the second link was a strong link I see it. Or am I missing your point?

[ronk]

I don't see how in your expression you obtain r4c5=9 => r9c9 = 9.

It's asymmetrical, more of an "odd pair" to me than an "equivalent pair."

(x) [r4c5]=[r4c9]-[r9c9]

Left-to-right:
If r4c5<>x, then r9c9<>x
If r4c5=x, r9c9 is indeterminate

Right-to-left:
If r9c9=x, then r4c5=x
If r9c9<>x, r4c5 is indeterminate

This asymmetrical property is not particularly attractive for nice loops IMO, but I'll wait to see how daj95376 uses it.

[daj95376]

Because I often encounter two cells that are either true/false together, what I want is to have a term for this relationship.

In the grid below, there are two cells that I'm calling an Equivalent Pair. It would appear that I need to provide two inference chains to fully qualify their relationship. I'd like to skip over these inference chains every time I run into a templates elimination like below.

Code: Select all

Equivalent Pair: [r4c8]<=>[r9c7] replaces ...

(x) [r4c8]=[r56c7]-[r9c7]
(x) [r4c8]-[r56c7]=[r9c7]

^-----------------------------------^
|  x  .  .  |  .  x  x  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  . +x  |
|  .  .  x  |  x  .  .  |  .  .  .  |
|-----------+-----------+-----------|
|  .  x  .  |  x  .  x  |  . -x  .  |
|  x  .  x  |  .  x  x  |  x  .  .  |
|  x  x  x  |  .  x  .  |  x  .  .  |
|-----------+-----------+-----------|
|  x  .  .  |  x  .  .  |  .  x  .  |
|  .  .  x  |  .  x  x  |  .  x  .  |
|  x  x  x  |  .  x  x  | -x  x  .  |
^-----------------------------------^   # GD01 from DanG


[udosuk]

Wouldn't it be more straightforward to write

Code: Select all

[r4c8]=[r56c7]=[r9c7]

Sorry if I've missed something obvious...

[ronk]

Equivalent Pair: [r4c8]<=>[r9c7] replaces ...

(x) [r4c8]=[r56c7]-[r9c7]
(x) [r4c8]-[r56c7]=[r9c7]

Ah ha! Using both "inference streams", it really is symmetrical and bidirectional. And if the candidates were colored, I could take any like-colored (grouped or ungrouped) candidates and say they were "equivalent?"

Doesn't coloring already have a term for that?

[wapati]

Doesn't coloring already have a term for that?

It would be easier for us if you would state it.