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tlanglet · Posted: Fri Jul 25, 2008 8:29 pm Post subject:

Well, I will be the first to suggest that this puzzle is VH+++, not VH+.

For me, basics consisted of two Box/Line interactions! I then found three finned x-wings and an xy-wing using my favorite techniques. I am now about to proceed to my next set of techniques. Wish me luck .......

Ted

Asellus · Posted: Sat Jul 26, 2008 2:46 am Post subject:

One of those colorings is particularly nice. However, I set for myself a different challenge: Could I solve this thing using only "finned" methods? And, given the nature of this puzzle, I can't say that this route was any more difficult than another! Here's the result:

[1] Finned X-Wing c15 r8c6<>2
[2] Finned X-Wing c17 r2c89<>7
[3] Finned X-Wing r39 r1c8<>7

Now, ignoring the XY Wing...

ravel · Joined: 21 Apr 2006 Posts: 536

Great solution, Asellus.

If you do use the x-wing in the last grid you can see the finned xy-wing 249 i had found.

nataraj · Posted: Sat Jul 26, 2008 11:32 am Post subject:

"Usual" methods (coloring, xy-wing and a 15 UR) get me to here:

ravel · Joined: 21 Apr 2006 Posts: 536

The UR 15 also eliminates 5 in r6c4, placing it r2c4. This gives an xyz-wing, which brings you here:

cgordon · Joined: 04 May 2007 Posts: 769 Location: ontario, canada

This is over my head. I thought for colouring you had to link up connected pairs (in boxes, rows and cols). I can't see any numbers where this is possible (at least for more than two pairs. Have I not gone far enough with the basics? Very confused and sorely troubled !!

(Edited Note: So far I used two ER's and a Finned x-wing (my first eh) to remove 2 from R8C6 and 7 from R12C8)

nataraj · Posted: Sat Jul 26, 2008 3:24 pm Post subject:

Thanks, ravel!

Sloppy work on that first UR, I should have taken out both 5s in col 4, of course.

Back on track again, I found the UR 46, xyz-wing and m-wing, and then another xyz-wing (4,8,9 box 1), which finally solved the puzzle... Smile

nataraj · Posted: Sat Jul 26, 2008 3:51 pm Post subject:

Craig,

after basics, which consist of only a few box/line interactions (as Ted remarked rightly), this is the position where coloring can help:

cgordon · Joined: 04 May 2007 Posts: 769 Location: ontario, canada

Nataraj: Thanks for the explanation. I can now see the Kite (which I had previously read about). It's just that this doesn't fit in with my neophyte understanding of colouring - which I thought was linking up a min. of 4 conjugal pairs (or whatever they are called). Though perhaps colouring (strong links with peers) is the basis for a multidude of patterns or solutions.
Thanks again
PS I had gotten one step further than your grid by placing a 9 in R1C8. using a Finned x-wing on 7. Also an ER removes the 2 from R8C6 and the 7 from R2C8.

nataraj · Posted: Sat Jul 26, 2008 6:06 pm Post subject:

Glad to have helped, Craig! I can see both the ER and the finned x-wing in the diagram for "7": the ER uses the strong link in row 9 and the group of 7s in col2/ box 1, the fin of the x-wing is in row 3 col 7. Amazing how different people look at the same sudoku grid in totally different ways... Myself, I do look for finned and other creatures, including ERs, swordfish et al., but only when the search for multi-coloring patterns turns up nothing.

I think the term coloring did indeed originate with a method where only strong links (only two cells in a house have x) were considered. On Andrew Stuart's site there is a good explanation of this basic coloring with very colorful graphics.

But he goes on to explain the more general concept of alternating weak and strong links in the section about X-cycles (part 1 and 2), which first introduced me to alternating inference chains (AICs) and "nice loops".
You don't have to completely understand the "theory". All one really needs is 3 simple rules
1. "strong"-"weak"-"strong"-...
2. begin and end with a strong link
3. a strong link can stand in for a weak link (and not the other way round)

Asellus · Posted: Sat Jul 26, 2008 9:58 pm Post subject:

Craig,

You might want to examine the <2>s in the early grid of this puzzle. There is another example of the "strong-weak-strong-weak-strong" string of links elimination. See if you can spot it.

The "strong-weak-strong" structure is the essential characteristic of the techniques variously known as Turbot Fish, Kite and/or Skyscraper. These are also the simplest examples of multi-coloring (when that central link is "weak only" and not a conjugate link substituting for the weak position, as nataraj pointed out is possible ... since in the all-conjugate case basic coloring suffices). As such, they are also examples of what some call a "Color Wing." Essentially, you can string two or more of these "Turbot Fish" things end to end, as we've done here. And, as long as you take care, as nataraj nicely explained, no explicit coloring is necessary.

As ravel hinted initially, this puzzle is interesting in that it had two examples of this sort of coloring, one in each of two digits.

cgordon · Joined: 04 May 2007 Posts: 769 Location: ontario, canada

keith · Posted: Sun Jul 27, 2008 2:56 am Post subject:

Marty R. · Posted: Sun Jul 27, 2008 3:52 am Post subject:

ravel · Joined: 21 Apr 2006 Posts: 536

nataraj · Posted: Sun Jul 27, 2008 5:20 pm Post subject:

Yes, too early. At this stage, there is only the one kite.
After the xy-wing and cleanup, this is where multi-coloring can be used again:

cgordon · Joined: 04 May 2007 Posts: 769 Location: ontario, canada

Yeah - got it at last (though I needed the hint). I had been looking for "formal" patterns eg Finned x wings. Thanks.

keith · Posted: Sun Jul 27, 2008 7:38 pm Post subject:

Marty R. · Posted: Sun Jul 27, 2008 8:12 pm Post subject: