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Asellus · Posted: Mon Apr 21, 2008 10:13 pm Post subject:

The way Clement describes his elimination of <5> in r1c2, it does sound like "forcing" reasoning. However, it isn't necessary to see it this way. Instead, the strong inference induced by the 48 UR between <5> in r1c3 and <3> in r1c5 is added to the end of a straightforward ALS Chain to provide the AIC elimination:
(5)r1c2-(5)r1c3=(3)r1c5-(3=5)r8c5-(5=8)r9c5-(8=7)r9c1-({17}=5)r79c2-(5)r1c2; r1c2<>5

In ordinary language: If r1c2 is <5>, then r1c3 is not <5> and r1c5 must be <3> (to kill the DP), then we XY Chain (via c5 and r9) to the <7> at r9c1. This "kills" the potential {17} pair in the r79c2 ALS, so one of those cells must be <5> and r1c2 cannot be. (This is the same as saying that the ALS becomes a {15} pair.) This contradiction means that r1c2 cannot be <5>.

[That ALS step could also be written -(7={15})r79c2-, which is easier to see following the chain in the direction I've written it. But, in the reverse direction, the "({17}=5)" notation is clearer. Either notation is valid and works. I chose the second to conform to Clement's reasoning.]

We have two different examples in this puzzle of how a UR/DP induced strong inference can be exploited in an AIC. While this is definitely overkill for these VH puzzles, exploiting such strong inferences can be very useful in more difficult puzzles.

AICs such as this are not really forcing, especially if uncovered by studying the alternating links. Medusa multi-coloring is, for instance, one way to do so. And without coloring, if one is comfortable with ALS Chains and strong links, then it is a tiny leap to either of these AICs.

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

keith · Posted: Mon Apr 21, 2008 10:47 pm Post subject:

Did this get explained?

keith · Posted: Mon Apr 21, 2008 11:01 pm Post subject:

nataraj · Posted: Mon Apr 21, 2008 11:07 pm Post subject:

keith · Posted: Mon Apr 21, 2008 11:50 pm Post subject:

George Woods · Joined: 28 Mar 2006 Posts: 304 Location: Dorset UK

This is the 3rd Vh in succession (I think) that can be solved by a W wing, when an XY or XYZ gave preety much the same next number!!

Asellus · Posted: Tue Apr 22, 2008 4:33 am Post subject:

cgordon,

Keith probably answered your question. But, if it helps you or others, the Kite in your <8> grid is marked below:

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

Asellus/Keith – thanks for the low-down on Kites or Turbot fish. I probably ignored investigating these before because I figured they were part of the family of Swordfish, Jellyfish etc - which I always found too difficult to locate. These kites however are remarkably simple – just a couple of skyscrapers at right angles originating from the same box. Even the diagonal variant isn’t that complex. Sometimes the solutions offered on this forum look like proofs for quantum physics. These kites however are definitely easy to follow.
PS: What was the original obsession with fish: Swordfish, Jellyfish, Squirmbags, Finned Fish, Turbot Fish ???

stevieboy · Joined: 25 Jan 2008 Posts: 31 Location: Michigan

Hi Everyone! I'm new at posting, but have been attempting the VH Sudoku puzzles here for awhile. In trying to solve this puzzle, I came across an XY-Wing which (I'm not sure) is really a legitimate XY-Wing??(!)
Is the 16-68-18 found in R3C4, R6C6 and R6C7 REALLY an XY-Wing eliminating the '8' in R5C4 ?? If not, why?

Thank you everyone for your constant daily mind-boggling output!! Laughing

storm_norm · Joined: 18 Oct 2007 Posts: 1741

keith · Posted: Tue Apr 22, 2008 8:16 pm Post subject:

nataraj · Posted: Tue Apr 22, 2008 8:19 pm Post subject:

To make matters worse (or maybe help by way of illustration), there is a valid xy-wing 168 in the puzzle. Look at r3c6, r6c6, r6c7.

The "pivot" cell in this case would be r6c6 (68), since it connects the other two.

The pincers are r3c6 (16) and r6c7 (18).

In an xy-wing, the digit present in both pincers ("1") can be eliminated from any cell that "sees" both pincers. The pivot cell sees both pincers and must contain the other two digits (6 and 8).

Unfortunately, in this puzzle, no cells that see both pincers contain any "1"s.

This is what is sometimes called a "useless" xy-wing.

nataraj · Posted: Tue Apr 22, 2008 8:20 pm Post subject:

synchronicity

storm_norm · Joined: 18 Oct 2007 Posts: 1741

Asellus, Keith, cgordon, nataraj... anyone who follows the coloring discussions,

wouldn't it be nice to have a "coloring function" on the Draw/play screen??

even if that isn't possible, maybe a function to only show a particular candidate, like all the 1's or 2's etc.

nataraj · Posted: Tue Apr 22, 2008 8:42 pm Post subject:

keith · Posted: Tue Apr 22, 2008 8:45 pm Post subject:

keith · Posted: Tue Apr 22, 2008 8:48 pm Post subject:

synchronicity

DennyOR · Joined: 12 Sep 2007 Posts: 33 Location: Portland, Oregon

Since I like to look for xy chains, from nataraj's position I solved the puzzle with what I would notate as (r3c8) 54-48-87-75=458=58 (r7c3), or what maybe would be called an xy chain with a coloring extension. Somebody a while back suggested looking for a coloring extension (my words) on an otherwise useless xy-wing (or chain), and that's turned out to be pretty useful.

stevieboy · Joined: 25 Jan 2008 Posts: 31 Location: Michigan

Thank you Keith, nataraj, and my "neighbor" in Michigan, storm_norm for educating me on the "pincer" concept...the XY-Wing examples I've seen were more like the ones you all described...I was "reaching" wrongly, no doubt about it!

There should be college classes on this stuff; sometimes wannabes, such as myself, need to have the solving methods drilled in our heads!