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Mogulmeister · Joined: 03 May 2007 Posts: 1151

Since nobody fancied this one I will have a pop.

This position arrives after a colouring/xy chain on 1 removes the 1 from r1c7.

Well here we are again: another fine example of "almost XY wing" which is also an ALS elimination and thanks to all who have been chipping in on this - I was very interested in your last comment Luke.

So we have an almost xy wing (in green) there is a fin at r3c2, a 1 which can be disposed of in 4 ways (that I can see):

1. If the fin is true then a contradiction is set up:

(68=1)r3c2-(1=5)r3c9-(5=6)r1c7-(6=1)r1c1 Can't have two 1s in block 1 so r3c2<>1

OR (if you prefer)

2. A nice ALS elimination

Set A is r1c17 = {1,5,6} Set B is r3c9 {1,5}

restricted common is 5 and common candidate 1 in r3c2 is toast.

OR

3/4. Of course there is an xy-wing or xy-chain (you choose) <156>

All different ways of looking at the same thing - whatever, xy-wing <168> is true and puzzle is solved.

peterj · Joined: 26 Mar 2010 Posts: 974 Location: London, UK

Mogulmeister,
On the ALS-XZ part, I presume you mean Set B is r3c9 (not 7)...?
But anyway, this is just a another simple xy-wing with vertex 56 at r1c8 and pincers at r1c1, r3c9?!
It is an ALS-XZ also of course - I think all xy-wings are.

[Edit] Sorry your post does say there is an xy-wing, didn't notice it, perhaps you edited it..

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Absolutely Peter ! Thanks. Will correct it.

[Edit]Yes it occurred to me just as I had posted so I added it for completeness!

Mogulmeister · Joined: 03 May 2007 Posts: 1151

peterj · Joined: 26 Mar 2010 Posts: 974 Location: London, UK

Yes, I think the whole class of techniques from xy-wing, xyz-wing, wxyz-wing, extended xyz-wing are also just special cases of ALS-XZ. Some people think of these techniques as 'bent triples' or 'bent quads' which reflects the ALS structure. Of course ALS-XZ is more powerful - I think the example in the 'fiery' puzzle is not solved by a standard "wing" technique
And of course when the second set is not just a pair then you are in a whole world of complexity...! Beyond me!

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Wondering into the world of Myth Jellies et al.......

Marty R. · Posted: Fri Apr 23, 2010 3:09 pm Post subject:

Kite (1) and two XY-Wings (561, 168).