SudoCue Users

Posted: **Fri Aug 24, 2007 2:56 am**

I'm not exactly stuck on this puzzle, but I do have a question about a technique I may have abused. This puzzle, according to sudocue, requires an XYZ-Wing and two hard steps.

This is the point where SudoCue uses an XYZ-Wing:

Code: Select all

.------------.------------.------------.
| 3   1   4  | 7   59  2  | 8   6   59 |
| 59  6   2  | 8   1   4  | 7   3   59 |
| 7   8   59 | 3   6   59 | 2   4   1  |
&#58;------------+------------+------------&#58;
| 2   7   59 | 1   4   6  | 59  8   3  |
| 8   3   1  | 59  7   59 | 6   2   4  |
| 59  4   6  | 2   8   3  | 159 19  7  |
&#58;------------+------------+------------&#58;
| 46  2   7  | *569 3&#40;5&#41;9 1  | 34  *59  8  |
| 16  5   3  | 4   29  8  | 19  7   26 |
| 146 9   8  | *56  235 7  | 34  1&#91;5&#93;  26 |
'------------'------------'------------'

I found the same wing SudoCue did, which I've starred (thanks, BTW for the pairs filter Ruud). We both eliminated a 5, but the 5's we eliminated were different. Sudocue's elimination is in parentheses, mine in square brackets. SudoCue's elimination required two more hard steps. My elimination sent the puzzle straight to singles. This is why I ask if I made a lucky mistake. I'm still trying to figure these wings out.

Posted: **Fri Aug 24, 2007 4:33 am**

It's a lucky mistake. The elimination cell for an xyz-wing has to see all three cells, not just the two wings. In this case, r7c5 sees all three and so the elimination of 5 is possible, but r9c8 only see two of the three cells and so the elimination does not follow from the pattern.

However, there is a move that will eliminate both 5's and hence crack the puzzle, namely an xy-chain

Code: Select all

&#40;5=9&#41;r7c8-&#40;9=1&#41;r8c7-&#40;1=6&#41;r8c1-&#40;6=2&#41;r8c9-&#40;2=6&#41;r9c9-&#40;6=5&#41;r9c4

and hence r7c45,r9c8<>5, solving the puzzle.

Posted: **Fri Aug 24, 2007 10:24 am**

Hi

The basic thing about xy-wings and xyz-wings and even ALS-xz eliminations is that the digit you try to eliminate has to see all instances of this digit present in the wing/pattern. For an xy-wing the digit you try to eliminate is only present in 2 wing cells. In an xyz-wing that digit is present in all three cells.

greetings

Para

Posted: **Fri Aug 24, 2007 6:57 pm**

Thanks for the kind and informative words. Makes a bit more sense now.

Funny you should mention the XY-chain (something else I've yet to tackle...need more patience), rep'nA. SudoCue used a Sashimi Swordfish and then an XY-Chain before the puzzle went to singles.

SudoCue Users

One-Trick Pony 8-23-07: Did I make a lucky mistake?

One-Trick Pony 8-23-07: Did I make a lucky mistake?