The New Sudoku Players' Forum

[ronk]

Havard, this thread was started by TKiel looking for help understanding coloring ... first with three strong chains ... and then with four strong chains.

That help is what I tried to provide. If you wish to use my example ... properly attributed, of course ... on your "Empty Rectangle thread", feel free to do so. But please stay on-topic here.

Thanks, Ron

[TKiel]

Ron,

Thanks much for the homework assignment. I'm still working on it. I'll have it on your desk by tomorrow. And thanks for pointing out that I was really only asking for an explanation about colouring, not for each and every and any way to make exclusions in the filtered digit. Maybe someday I'll be ready to tackle the stuff to which Carcul and Havard refer, but not yet. I would add that, even though their posts were off topic, they were not uninformative.

Tracy

[Havard]

hi
I don't see why this is so terribly off topic:

So my point was that using 4 strong links seemed at least one too many! I have actually yet too see a puzzle that needs 4 strong links to solve. Even the classic "needs jellyfish" puzzle from ages ago can be solved with just three strong links... So in my opinion, Tracy is right in saying that:

In general, would it be safe to say, that no matter how many different conjugate chains exist, only three at a time, but not necessarily the same three, can be linked in such a manner that would possibly lead to an exclusion? And the only real advantage to more chains is more different three chain connections?

At least your example did not disprove this.
havard

[ronk]

So in my opinion, Tracy is right in saying that:

In general, would it be safe to say, that no matter how many different conjugate chains exist, only three at a time, but not necessarily the same three, can be linked in such a manner that would possibly lead to an exclusion? And the only real advantage to more chains is more different three chain connections?

At least your example did not disprove this.

Since I didn't notice eliminations could be made with only 3 conjugate chains, it wasn't a good example. A better example is puzzle #41 of the top1465.

Code: Select all

 4.3|5..|.2.
 ...|.16|...
 7..|...|...
 ---+---+---
 ...|.89|5..
 ...|3..|8..
 2..|...|...
 ---+---+---
 ...|4..|.7.
 .9.|...|6..
 .1.|...|...

With basic techniques can be advanced to:

Code: Select all

 4      68     3      | 5      9      78     | 17     2      1678
 589    258    2589   | 278    1      6      | 347    3458   34578
 7      2568   1      | 28     34     34     | 9      568    568
----------------------+----------------------+-------------------- 
 13     347    6      | 17     8      9      | 5      134    2
 159    457    59     | 3      2457   12457  | 8      1469   1467
 2      34578  589    | 6      457    1457   | 1347   1349   1347
----------------------+----------------------+-------------------- 
 3568   2358   258    | 4      356    1358   | 13     7      9
 358    9      47     | 178    2357   123578 | 6      13458  13458
 3568   1      47     | 9      3567   3578   | 2      3458   3458

With 1s color map ...

Code: Select all

 . . . | . . . | A . a
 . . . | . . . | . . .
 . . . | . . . | . . .
 - - - + - - - + - - -
 C . . | D . . | . 1 .
 c . . | . . 1 | . 1 1
 . . . | . . 1 | 1 1 1
 - - - + - - - + - - -
 . . . | . . B | b . .
 . . . | d . 1 | . 1 1
 . . . | . . . | . . .

... for elimination r5c9<>1 at the intersection of colors 'a' and 'c'. While it can be mathematically proven that A!C (A true excludes C true) and C!A, it is easier just to follow the alternating strong and weak links of the discontinuous x-cycle of length 9.

Ron

P.S. In your earlier post, I interpreted ...

Code: Select all

. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
- - - + - - - + - - -
9 .-9 | . 9 9 | . . .
| . 9-------------9 .
| . . | . 9 . | 9-9 .
| - - + - - - + | - -
| . . | . . 9 | | 9 .
9 . . | .-9-9 | 9 . .
. . 9 | . 9 9 | . 9 .

... to be another grouped candidate x-cycle, instead of the simple continuous x-cycle of length 6 it is. Sorry.