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Marty R. · Posted: Wed Oct 15, 2008 3:40 pm Post subject: Vanhegan Extreme

Random 6-627799, rated 2.1.0.1.1.

nataraj · Posted: Wed Oct 15, 2008 6:12 pm Post subject:

kite (1) row 1, col 1 => r4c7<>1
kite (6) row 7, col 7 => r2c2<>6

Here:

daj95376 · Joined: 23 Aug 2008 Posts: 3854

From nataraj's PM:

storm_norm · Joined: 18 Oct 2007 Posts: 1741

or do the generalized m-wing first then a xy-wing finishes it.

Marty R. · Posted: Thu Oct 16, 2008 12:29 am Post subject:

nataraj · Posted: Thu Oct 16, 2008 5:45 am Post subject:

Marty,

what I call a "generalized" m-wing, is

- what Keith called "Appendix: ravel's half M-wing" in this thread
- without the restriction that the first and third cell in the chain must be identical.

The "classic" m-wing would look like this:

12-12-12=(2)=28

It forms two "pincers" - the cells containing 12 and 28 - and no cell that sees both pincers can contain 2. (I mark the pincer cells with "*").

The half m-wing is very similar, except that the second cell doesn't have to be identical to the first and third cells. BUT, there has to be a strong link on 1 between second and third cell. It would look like this:

12-128=(1)=12=(2)=28

It works exactly the same way as the classic m-wing

The "generalized" m-wing removes the restriction that first and third cell must be identical. The wing still works exactly the same way: if the first cell is "1", then the third cell is "1", then the fourth cell must be "2"

12-128=(1)=126=(2)=28

I mark the two "helper" cells (the ones with the strong link on 1) "#"

For a somewhat longer explanation, see this thread

daj95376 · Joined: 23 Aug 2008 Posts: 3854

[Withdrawn: After reading keith's reply, I realize that I was mistaken in thinking that the M-Wing was limited to four cells.]

Marty R. · Posted: Thu Oct 16, 2008 3:59 pm Post subject:

Thanks Nataraj and Dan.

storm_norm · Joined: 18 Oct 2007 Posts: 1741

I'll provide the picture this time. you will see in the generalized M-wing that the third cell ( the cell that would normally house the same pair in the first cell) does have both candidates present. the difference is that because the link is weak within the cell that the cell can have more than just the two original candidates.

because you would think in your head
first cell: is not 2, must be 1
second cell: is not 1
third cell: has to be 1, cannot be 2 (and cannot be any other candidate in the cell)
fourth cell: has to be 2 (hence why the 2 in r1c5 can be eliminated)

so in the image above you can see the strong links in green on candidate 1.

the blue link is the strong link on 2 needed from r3c1 because if r3c1 is 1, then it can't be 2... that means r3c5 has to be 2.

and going in reverse, you would think in your head if r3c5 is not 2, then you would find that r1c7 has to be 2.

and just to go a little further... if that 6 in r3c1 were strongly linked anywhere else in the puzzle, it would be tempting to see what other eliminations could be made by seeing where the sprawling arms lead.

daj95376 · Joined: 23 Aug 2008 Posts: 3854

[Withdrawn: After reading keith's reply, I realize that I was mistaken in thinking that the M-Wing was limited to four cells.]

Aaaaaagh!!!

nataraj · Posted: Thu Oct 16, 2008 9:46 pm Post subject:

daj95376 · Joined: 23 Aug 2008 Posts: 3854

[Withdrawn: After reading keith's reply, I realize that I was mistaken in thinking that the M-Wing was limited to four cells.]

keith · Posted: Thu Oct 16, 2008 11:35 pm Post subject: I disagree, I think

I only have a few minutes, but let me say a couple of things.

(Strong link =, weak link -)

An M-wing starts with a complementary pair. Two cells that have the same two candidates, plus the knowledge that they have the same value.

XY ..?..XY

If the first and last cells are A and B: The value in A implies the same value in B, and vice-versa.

Now, suppose we can append a strong link on either X (or Y) at one of the ends:

XY ..?..XY = aX

where a is anything. Now we have A, B, C. If A is X, the value of C is immaterial. If A is Y, C must be X.

So, A and C are pincers. Any cell that sees both cannot be X.

So far, so good?

How are A and B connected to know they are the same? My original idea was that it does not matter. In the simplest case there are strong links on Y:

XY = bY = XY = aX

where b is anything. If you think about this long enough, you will realize that Medusa coloring will ALWAYS find this chain, hence the name "M-wing".

Two points:

1. XY = XY = XY = aX is, to me, not the simplest case of an M-wing. It is coloring on X.

2. Ravel's half-wing is a very astute observation that you may have A implies B, but B does not imply A. So,

XY - bY = XY = aX

makes the same eliminations as an M-wing.

Keith