dailysudoku.com

[nataraj]

One single xy-wing.
Doesn't seem to do much (removes 3 out of a cell with 5! candidates {3,4,7,8,9}).

But it solves the puzzle.

Better fill in your PMs, guys....


Hm ... Is that a semi-O-wing then?

_______

For you friends of w-wings out there:
(8)r1c8= [83-35-57-76-63-38] =(8)r9c7; removes a LOT of "8"s in r7c8 r1c7 r2c7 r3c7.

[keith]

There are two UR's, but they don't solve the puzzle. Here is the grid after basics:

[Asellus]

keith and nataraj,

You are both right. It is a W-Wing via that XY Chain: one or both must be <8>. And, via the single {38} bivalue, both must be <3> or both must be <8>. The only option that satisfies both demands is: both must be <8>, which is indeed the case.

[cgordon]

I used a UR <79> R35 to leave <58> in R3C5
then a <589> xy-wing; pivot <89> in R2C7 that removed <5> in R2C5
then another UR <49> in C79
then a <358> xy-wing; pivot <58> R9C2 that removed <3> from R3C7

Sure - it could have been done in one step - but I had fun !!

BTW. I am very pleased to see something like 6 VHs in the last 10 days. Thank you. That's the way it should be. Let the plebs get their easy puzzles in the tabloids and leave this Forum to the sophisticates like what we are.

[Marty R.]

[keith]

[nataraj]

no problem, keith. And thanks, Asellus for your explanation. I can see that the "shorthand" notation for my xy-chain was too confusing. I was just too lazy to note all the steps in the chain with r1c3 ...

And to avoid any other misunderstanding: my xy-wing was 35-58-38 with pivot r9c2. It tkes out the "3" in r3c7 which makes 3 in r3c2 a hidden single.

[nataraj]

[cgordon]

[nataraj]

[Marty R.]

[mckeann]

All the explanations make sense, but i'm damned if i can spot the pattern without a clue from here

[Marty R.]

[storm_norm]

geez, if i would have read the forum first I would have not gone through two ur's and some coloring only to find out that it has one step.

so this puzzle had a one "major" step life expectancy.

been a few VH's that didn't have a very long life expectancy.

[mckeann]

[Marty R.]

[nataraj]

[Asellus]

mckeann,

Perhaps you are referring to Keith's "extended XY Wing," which is actually a particular instance of an XY Chain, that removes the two <5>s. It involves the following cells in sequence:
r1c3 - r1c8 - r7c8 - r9c7 - r9c2
And, it works in this way:
(1) If r1c3 is <5>, then r3c2 and r9c3 cannot be <5>. (And we have no idea what r9c2 is.)
(2) If r1c3 is NOT <5>, then it is <3> and r1c8 is <8> and r7c8 is <3> and r9c7 is <8> and r9c2 is <5>... and r3c2 and r9c3 cannot be <5>.
So, since either (1) or (2) must be true, then one or both of r1c3 and r9c2 must be <5> and r3c2 and r9c3 can never be <5>.

A similar XY Wing would have a {35} - {38} - {58} structure. Because two more {38} cells occur in the middle, Keith called it an "extended" XY Wing.

[Edit: nataraj's post wasn't there when I started this. Well, two heads are better than one!]

[keith]

I think Neil is complaining that he sees the cells, but does not recognize the pattern.

Any time you have three cells with the same pair of candidates that form two strong links, you should look for opportunities. The chain fragment is

XY=XY=XY

and, in the solution, each end has the same value, X or Y.

In this case, Marty and I used it to extend an XY-wing. The regular XY-wing is

XZ-XY-YZ

with pincers Z. (Any cell that sees both ends cannot be Z.) The extended wing is

XZ-XY=XY=XY-YZ

and has the same pincers, Z.

You can also possibly extend the end of an XY-wing:

XZ-XY-YZ=YZ=YZ

Another possibility is a step in Medusa coloring. Is there a strong link in either X or Y on one end? For example,

X=XY=XY=XY

is a chain that has X as pincers.

[Edit: Actually, this last one is simple coloring on X. The Medusa chain is

X=XY=Y=XY

and has X as pincers.]

Keith

[Marty R.]