dailysudoku.com

[Earl]

Today's puzzle was not challenge enough, so . . .

[TKiel]

There's a naked pair in box 2, not that it gets one very far. After that there are W-wings, a finned X-wing and coloring that reduce the PM's somewhat.

[Asellus]

Very interesting puzzle. For me, the key lay in the <2>s. Apart from a Finned X-Wing at the start, all the other steps I used involved eliminating <2>s. Two of those steps were very interesting Color Wraps.

I'll give others a chance to ruminate before posting my steps.

[Marty R.]

[TKiel]

[Earl]

I used your tips to find a w-wing (pincers R1C5, R4C6) and the finned x-wing (eliminates 1 from R4C8) to arrived here. There is only one strong pair of 2's. I can't see how to eliminate any. A hint?

Earl

[Asellus]

Oops! I mistakenly wrote "Color Wrap" in my prior post. I meant to write "Color Wing"!

I also have a bad habit of saying Color Wrap when I mean simple Coloring (also known as a Color Trap) on a single digit. In simple Coloring, the opposite polarities of interconnected strong links for a digit are noted and any candidates which can "see" instances of opposite polarity are eliminated.

(I used Coloring in the solution, also. I try to avoid the term Color Wrap.)

A Color Wrap is a special instance of simple Coloring in which a polarity contradiction is discovered, i.e. two cells of the same polarity (color) are discovered in a single house, which is not possible. In these cases, all instances of the conflicting polarity can be eliminated and the other polarity values placed. These don't occur very often.

A Color Wing is a bit more complicated. I believe some people refer to it as two-strand coloring, or something like that. One selects a "Bridge," which is a weak link on the digit, and then two separate strong link Coloring strands are formed from each end of the Bridge with the two bridge cells having the same color. Eliminations occur when a cell can "see" the polarity (or color) opposite that of the bridge from each of the two coloring strands.

Often, Skyscrapers, 2-String Kites and some other named techniques are special instances of Color Wings. (Some of them can also be instances of simple Coloring.)

I plan to post my solution later tonight, which will show how the Color Wing works.

Here is a link to the explanations at Ruud's Sudocue site:

http://www.sudocue.net/guide.php#ConnectedPairs

The explanation is a bit lengthy, but eventually gets around to all of these techniques.

[Asellus]

Earl,

I didn't use the <1> Finned X-Wing. There is another one that will help you. But you need to do that naked 24 pair simplification in Box 2 in order to see it.

[Marty R.]

Thanks. The Color Wrap with two cells in a house with the same polarity has been discussed here on one occasion that I recall, but the poster (Tracy, I think) didn't have a separate name for it.

If I correctly understand the Color Wing, that is what is commonly referred to as multi-coloring.

[Johan]

Earl,

This one is a tough one.
You can use the strong links on <2> in Box 2 for eliminating several <2>'s in Box 4


Johan

[Asellus]

Marty,

I find the term "multi-coloring" ambiguous: Medusa Coloring is also known as "multi-dimensional coloring" since it colors on multiple digits.

Even the terms "two-strand" or "multi-strand" coloring are ambiguous since there also exist Medusa Wings, which are two-stranded multi-dimensional coloring! (Phew!)

I prefer to follow Ruud's nomenclature and use Color Wing when there is a bridge and two-strands with single-digit coloring and Medusa Wing for the analogous multi-digit coloring.

The Wing name makes sense to me if the bridge is considered as the pivot. All "Wing" named technigues involve pincer branches (wings) from a pivot of some sort.

[Asellus]

Here is my solution to Earl's puzzle. First, however, I discovered a flaw in one of my "I'm only using <2>s" steps (which worked, as it happened, accidentally), so had to revise the final parts of the solution and resort to some other digits. Still, the <2>s are central. It was a tough nut to crack.

After the 24 Naked Pair (Box 2), the first two steps have already been mentioned:

1: the Finned X-Wing in C47 (eliminates <4> in R3C9)

2: the 24 W-Wing in C56 (eliminates <2> in R5C5). At this point, all of the <1>s are fixed and simplifications expose...

3: XYZ-Wing: Pivot R6C9, eliminates <2> in R6C7

4 and 5: A couple of related Color Wings

[TKiel]

[Asellus]

[nataraj]

------- the Cheshire Cat way

[TKiel]

[Asellus]

nataraj,

I don't believe those Color Wings are really all that elaborate... apart from the little conjugate Box-Row bit in these particular instances. Elsewhere you've posted much the same thing, though limited to "wings" of single strong links. Perhaps it would help make them easier to see by using your "dot diagram" approach:

[Asellus]

As Tracy says, Coloring is not forcing. And, Coloring on a single digit is easy to do and is often useful.

On this board, we rarely see multi-digit Coloring (a.k.a. Medusa Coloring). That might be because it can get very extensive and other, more commonly used options are often possible. However, if one is tempted to resort to forcing, it can be worth trying some Medusa Coloring first. It isn't always extensive or messy.

For instance, it can provide an elimination in the R6C7 cell involved in nataraj's forcing. Start by noting that there are several bivalue cells involving 2, 5 and 8. So, pick one and start coloring. The bivalue strong links allow the coloring to spread to multiple digits:

[nataraj]

Thank you, Tracy and Asellus!

Thank you so much indeed - your post especially Asellus made me look at coloring in a completely new light. I used to think one would color the whole cell (as it is shown in so many explanations on the net) when in fact you go and color the indiviual candidates in the pencil marks.

Bear in mind I do sudoku on paper only and my main problem with forcing and coloring as I understood it up to now is that once you've started the grid is changed for good and if it turns out the initial choice was a dead end you've had it.

Now I understand that green really means all candidates that belong together in one implication chain and red belong to the other, much like my "left" and "right" but without scribbling into the grid.

Really makes it much easier to see relationships.

I'll look at color wings again, I promise.

[Marty R.]