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Clement · Posted: Sun Aug 22, 2010 10:31 pm Post subject: Aug 23 VH

XY-Wing 56 75 67 with Pivot in BOX 5 eliminates 6 in r1c4 solving the puzzle.

Marty R. · Posted: Mon Aug 23, 2010 1:03 am Post subject:

The XY-Wing works as both a 567 or 576. Also, either of two different W-Wings on 67 pairs in boxes 28.

kuskey · Joined: 10 Dec 2008 Posts: 141 Location: Pembroke, NH

I used two 567 xy-wings, first with a pivot in r6c6 deleting 5 in r4c3 followed by the one Clement mentioned.

Stuart · Joined: 23 Aug 2010 Posts: 2

Learned quite a bit from this site but todays puzzle confuses me in one of the rules. R2C7 with pincers in R2C5 and R8C7 should eliminate the 6 in R6C7 but does not, why doesn't the rule work this time?
thanks

Marty R. · Posted: Mon Aug 23, 2010 11:42 pm Post subject:

Stuart · Joined: 23 Aug 2010 Posts: 2

Marty,
I needed to find the rule name, it is XYZ wing and in this puzzle would be the 67, 467 and 46 in r2c5, r2c7, and r9c7.

Marty R. · Posted: Tue Aug 24, 2010 1:23 am Post subject:

tlanglet · Posted: Tue Aug 24, 2010 2:59 pm Post subject:

Hi Stuart and Marty,

Marty: I believe that the pattern you selected to illustrate an xyz-wing if r8c8 did not contain a 4 is really a valid "almost" xyz-wing.

Stuart and Marty: Think of the 4 in r8c8 as a fin similar to a finned x-wing condition. For the finned x-wing, we logically, if not mechanically, proceed in two steps:
If the x-wing is true (that is the fin is not present) then what is deleted, and then
If the fin is true, then what does it delete.
All deletions common to both conditions may be deleted. For the finned x-wing, the common deletions are the two row/column cells in the box that contains both a corner cell of the x-wing and the fin cell.

For any "almost" pattern, we can proceed in the same two steps, but the determination of what is deleted by the fin is more involved. (When applied to a x-wing where the fin does not share a box containing a corner cell, the pattern is called a Kraken finned x-wing.)

So consider the suggested "almost" xyz-wing with (567) in r8c5, (67) in r9c6 and the (456) in r8c8 considered as two parts: either r8c8=56 or r8c8=4.
If the xyz-wing is true, then consider r8c8=56,
If r8c5=5, then r8c8<>5=6, then r8c4<>6
If r8c5=6, then r8c4<>6
If r8c5=7 then r9c6<>7=6, then r8c4<>6
Thus, if the xyz-wing is true, r8c4<>6

Now handle the fin 4 in r8c8
If r8c8=4 then r2c8<>4=6, then r2c5<>6, then r1c4=6, then r8c4<>6
Thus, if the fin 4 in r8c8 is true, then r8c4<>6

To summarize, cell r8c8 must equal 56 or a 4, and we have shown that both conditions delete the 6 in r8c4. Jackpot!!

I am not a good instructor, but hope this example is more helpful that confusing. Please do not hesitate to inquire on any issue that is of concern.

Ted

Marty R. · Posted: Tue Aug 24, 2010 4:07 pm Post subject:

Ted,

Your points are well taken. However, as you know, I'm not a fan of the "almost" techniques for the most part.

Regardless, my point was only to illustrate what an XYZ-Wing pattern looks like and what could be eliminated as a result. Stuart was asking about the basic XYZ-Wing technique and I was just trying to help him out with it.