dailysudoku.com

[Asellus]

Craig,

I believe there is a little bit of working at cross purposes going on here. Keith's interest seems to be in finding useful patterns involving chains of repeating identical bivalue cells (remote naked pairs, extended XY Wings, etc.). And that's all well and good.

However, if your interest is in pincer coloring, then I suggest it is better to forget about bivalue chains and focus on the coloring. Coloring from a pincer is just a matter of using any sequences of end-to-end strong links that are available. It doesn't matter if the cells along the way are bivalues.

So, not only does that {48} cell with the transported pincer in my example not need to be {28}, it doesn't even need to be a bivalue. It could be {24789} and still work, provided that <8> is strongly linked to the <8> at r1c5.

Another nice thing about thinking in alternating colors (red-green) along the "color chain" is that you don't have to remember if it is odd numbers or even numbers of links, nodes, whatever. Just keep track of the colors.

Pincers can also be transported by means of one or more ERs, if you are comfortable with that idea.

You should only transport/color extend one pincer (of a pincer pair) and perform the eliminations against the other pincer. (While it is possible to color from both pincers at the same time, the coloring rules are a bit more involved. So, I wouldn't recommend it unless you are confident you understand the rules for such things.)

By the way... I wouldn't abandon the ideas of chains so completely. They can be useful and aren't really so difficult if, in my opinion, you learn the general rules for chains rather than trying to memorize set chain patterns. But, that's for another day, I'm sure.

[alanr555]

[Asellus]

Alan,

This thread doesn't seem the place for lots of theoretical discussion; but, I'll try to give a brief reply to your points as I see them.

First, I'm all in favor of pattern solutions such as the "fish" methods and XY-Wings, Kites, etc., exactly because there is nothing "mathematical" about them. Most of these techniques involve patterns that are easy to recognize and use even if one does not fully understand how they work. They are by far the most popular and widely used methods by ordinary folks who have no interest in learning any "theory."

My response to Craig about patterns applies only to implication chains. In that case, I believe it is easier to learn and apply the basic rules for AICs than it is to try to memorize various patterns for chains (such as "xz-xy-yz=yz=yz").

As for the use of implication chains for solving puzzles, I believe it makes sense to try to exhaust the pattern techniques first, using chains as a "last resort" for the most difficult puzzles. This also means that learning the pattern techniques is a higher priority.

"Coloring" is a general term for a variety of related methods. I'd say that your statement is backwards: it seems more accurate to me to say that implication chains are another way to view coloring. All coloring can be expressed as implication chains (as can virtually all of the sudoku techniques) but a great many implication chains cannot be captured using coloring.

Pencil solvers tend to avoid coloring because of the problem of making color marks. But many simple cases can be done in ones head without marking. Also, using blank grids to mark the locations of all cells for a single candidate digit is useful both for coloring and other pattern methods. Multi-digit "Medusa" coloring poses the biggest challenges to pencil solvers. But, it is also the most powerful of the coloring techniques.

I don't have any specific links to provide. However, searching sudopedia.org or the solving guide at sudocue.net are two possible places to begin looking.

[Marty R.]

[mjchamorro]

Hello Everyone:

This is where I got stuck in daily sudoku from 21-Dec-2007.

3 248 1|45 258 6|45 9 7
6 24 7|1459 259 124|345 345 8
5 48 9|3 7 48|6 2 1
-------------------------------------
9 135 35|7 26 24|8 14 56
4 6 2|8 1 5|9 7 3
7 15 8|469 69 3|2 14 56
------------------------------------
1 9 356|56 4 78|357 3568 2
2 35 4|156 3568 178|357 3568 9
8 7 356|2 356 9|1 356 4

The thing is that when I ask for a hint in the draw/play section on dailysudoku, I'm given this hint:
r4c5=6

My question is WHY is that the next logical step?

thank you for any help or advise.

María José

[Steve R]

Hi, and welcome

[mjchamorro]

Thank you steve, now i just have to find out what a xy-wing is. I knew about the x-wing and the swordfish, but not xy-wing...

anyway thank you very much, really, now there is light at the end of the tunner

[Steve R]

Glad to be of help.

You may find SadMan’s explanation of the xy-wing helpful, as I did.

Steve