## Overlapping XY-Wings

Everything about Sudoku that doesn't fit in one of the other sections

### Overlapping XY-Wings

While updating my XY-Wing() function to use Buddy Lists, I ran across a discrepancy when comparing previous results against current results on this puzzle. Upon closer examination, I discovered two XY-Wings off of the same pivotal cell -- r4c3 <#>.

Now, an XY-Wing can be generated from <#> with the value <6> through the <a> cells to cause an elimination in the <A> cell. Or, an XY-Wing can be generated from <#> with the value <7> through the <b> cells to cause eliminations in the <B> cells.

Whichever XY-Wing is selected, the puzzle can then be solved without the need to find the other XY-Wing.

Does anyone have any experience with overlapping XY-Wings? If so, then do you have any idea on the frequency of it happening?

Code: Select all
`*--------------------------------------------------*| 1    4    6    | 9    3    5    | 8    7    2    || 3    7    9    | 2    1    8    | 6    4    5    || 8    5    2    | 7    4    6    | 19   3    19   ||----------------+----------------+----------------|| 579B 69   58#  | 1    78b  2    | 4    56a  3    || 4    68a  1    | 5    9    3    | 2    68A  7    || 57b  2    3    | 6    78B  4    | 59   1    89   ||----------------+----------------+----------------|| 6    1    48   | 3    5    9    | 7    2    48   || 2    3    45   | 8    6    7    | 15   9    14   || 59   89   7    | 4    2    1    | 3    58   6    |*--------------------------------------------------*`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

i've seen it quite a lot. Here's a good example with 3 xy-wings in very close proximity:
Code: Select all
` . . . | 9 . 2 | . . .  5 . . | . . . | . . 3  . . 9 | . 4 . | 8 . .  ------+-------+------  8 . . | . . . | . . 5  . . 5 | 7 . 6 | 4 . .  . . . | 1 . 3 | . . .  ------+-------+------  . 4 . | 8 . 1 | . 3 .  . . 8 | . . . | 7 . .  . 7 . | . . . | . 9 . `

it happens towards the end of the puzzle, you have to wade through a couple of xy wings before it appears
ab

Posts: 451
Joined: 06 September 2005

ab,

Thanks for the info. I must admit surprise at its commonality.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006