xy_wing question

retired43male · Posted: Thu Jun 07, 2007 12:32 pm Post subject: xy_wing question

Please hang with me on my first post. I have the book Solving Sudoku by Gordon and ran into a "how come" question on puzzle 729 in his book.

The puzzle lays out like this:

59 679 4 57 8 1 2 3 69

58 678 1 3 2 9 47 4567 46

23 79 23 457 67 46 1 574 8

I found the xy, 59, 57, 79 and drew my little chart. My first reaction was to eliminate the 9 from the cell 679. Then I saw all the 7's that I could get rid of. Leaving me just a 6 in the second cell. Being kind of new, I checked the ans page before speeding to the finsih and found out the 9 was really the solution to the cell 679.

Can someone explain where my learning/thought process has gone wrong on the xy wing.

thanks
bob

Jean-Christophe · Posted: Thu Jun 07, 2007 5:11 pm Post subject:

You'll find explanations here : http://www.sudopedia.org/wiki/XY-Wing

I assume this shows the top 3 rows. Your example is case 1. The pivot is R1C1={59}, the pincers are R1C4={57} and R3C2={79}. The logic is: whichever the digit goes in the pivot, there is a 7 in one of the pincer (R1C4 or R3C2). Therefore we may eliminate 7 from R1C2, R3C4 and R3C5 (leaving a naked single 6 in R3C5)
_________________
Jean-Christophe
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." Sherlock Holmes.

retired43male · Posted: Thu Jun 07, 2007 6:20 pm Post subject:

ok I think I see what you are saying. I'll play more and see how it works. XY wings have never been clean to me, but this may help, thanks again

bob

north55 · Posted: Thu Jun 07, 2007 9:04 pm Post subject:

This is the way I look at it. It is a "naked triple", but bent.

The normal naked triple is in a row or column.
If one pair of the trip is off the column/row then it may be an xy wing.
The "off" cell needs to be visible to ONE of the other two.

retired43male · Posted: Fri Jun 08, 2007 1:18 am Post subject:

WOW, that is so simple, thanks

Mosc_007 · Posted: Fri Jun 08, 2007 4:43 pm Post subject:

xy wing did take some time to sort out. They are fun now. They become so obvious after you have plaed with them quite a lot. Swordfish is another fun one although you dont get them often.

Charles