X-Wing

Advanced methods and approaches for solving Sudoku puzzles

X-Wing

Postby jeanboucher » Sat Aug 05, 2006 4:38 am

Can someone help me find how to spot an X-Wing formation

This one have an X-Wing formation for the {1}

Image

I don't see it !!!

Thanks

I have read several explanations & I still don't get it!
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Postby RW » Sat Aug 05, 2006 6:35 am

First, look at column 4. There's exactly two cells where digit 1 can go in that column (row 3 and row 5). Then look at column 7, the only two cells for digit 1 in that column are also row 3 and 5. Now think, what would happen if digit 1 went in anywhere else in either of rows 3 or 5?

Hope this helped.

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X-wing

Postby keith » Sat Aug 05, 2006 11:10 am

Look at C4. There are only two places <1> can go: R3 or R5. One or the other must be <1>.

Look at C7. There are only two places <1> can go: R3 or R5. One or the other must be <1>.

Now, look at the rectangle with corners R35C47. Two corners of this rectangle must have the value <1>, and they must be diagonally opposite each other. (You don't know which diagonal.)

So, the <1> in R3 and the <1> in R5 lie on a corner of the rectangle. You can eliminate <1> as a candidate in all other cells in these rows.

In other words, eliminate <1> from R3C359 and R5C35.

I hope this helps.

Keith
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Postby jeanboucher » Sat Aug 05, 2006 12:33 pm

Thank you guys!

So the rules for an X-Wing formation is:
MUST BE ONLY 2 candidates on the same Column in 2 diferent Rows in a box formation.
Or
MUST BE ONLY 2 candidates on the same Row in 2 different Columns in a box formation.
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X-Wing

Postby Cec » Sat Aug 05, 2006 2:23 pm

jeanboucher wrote:"....So the rules for an X-Wing formation is:
MUST BE ONLY 2 candidates on the same Column in 2 diferent Rows in a box formation.
Or
MUST BE ONLY 2 candidates on the same Row in 2 different Columns in a box formation.

Hi jeanboucher...Your explanation suggests you do understand what the X-Wing pattern is although your wording is somewhat unclear in referring to the candidates appearing only in the same row (or the same column).

IMHO I find the following definition, courtesy of angusj, more clearly describes this particular pattern:

An X-Wing requires a particular candidate to appear twice and only twice either in two rows and sharing the same two columns in which case the eventual exclusions occur in columns or, using the same logic, where the particular candidate appears twice and only twice in two columns and sharing the same two rows then the exclusions occur in rows..."

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Postby udosuk » Sat Aug 05, 2006 2:30 pm

Perhaps rewrite it a little bit:

The Rewriter wrote:So the rules for an X-Wing formation is:
THE CANDIDATE MUST APPEAR ONLY TWICE on the same 2 Columns on each of 2 different Rows in a box formation.
Or
THE CANDIDATE MUST APPEAR ONLY TWICE on the same 2 Rows on each of 2 different Columns in a box formation.
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X-Wing

Postby Cec » Sat Aug 05, 2006 3:33 pm

udosuk wrote:Perhaps rewrite it a little bit:

The Rewriter wrote:So the rules for an X-Wing formation is:
THE CANDIDATE MUST APPEAR ONLY TWICE on the same 2 Columns on each of 2 different Rows in a box formation.
Or
THE CANDIDATE MUST APPEAR ONLY TWICE on the same 2 Rows on each of 2 different Columns in a box formation.

I agree this is a shorter definition but personally I think the wording of "box formation" might be confusing, particularly to newcomers, because the Forum's recommended terminology basically defines the "box" as a 3X3 grid. Whilst not strictly defining the X-Wing pattern, I also thought it important to include where the candidate exclusions occur for either of the above two criteria.
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Postby jeanboucher » Sun Aug 06, 2006 5:34 am

Thank you for the reference Cec.

I agree with you, the definition you provide is far better then the one I came with, but...

I was not trying to write a new definition, I was just trying to understand the patern.
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X-Wing

Postby Cec » Sun Aug 06, 2006 9:44 am

jeanboucher wrote:"....I was not trying to write a new definition, I was just trying to understand the patern.

Thanks for the feedback jeanboucher and no.. I never thought you were trying to write a new definition for an X-Wing pattern.

For what it's worth, you will see from clicking on HERE all the problems I had in trying to understand the X-Wing pattern:) I now understand the pattern but trying to spot the "little devils" is still a problem for me.

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