dailysudoku.com

[sheryl]

`well, everyone. that did it. the 9 in box 4 and the 2 in box 9 ended up doing all the ensuing elminations, so i will be very careful from now on. though i still want to understand x wings and xy wings and swordfish and the entire repertoire of techniques.

keith, in response to what you've written:

here's what you have: the tab is the number that i have

. R6C9 is the only square in row 6 that can be <8>. 7
b. R7C6 is the only square in column 6 that can be <2>. 1
c. R6C7 is the only square in column 7 that can be <2>. 2
d. R6C8 is the only square in column 8 that can be <3>. 9
e R9C8 is the only square in column 8 that can be <4>. 2
f. R7C9 is the only square in column 9 that can be <1>. 9
g. R4C2 is the only square in block 4 that can be <9>. 9

so if your's works and mine works, then there are two solutions to this puzzle. does anyone (or everyone) agree with that.

[kragzy]

Keith,

Not to labour it, but take your first statement - the <8> in C9 is already solved (R9C9), so "R6C9 is the only square in row 6 that can be <8>" is patently wrong. But enough of that.

Sheryl,

The way I go about looking for XY wings is this (it's methodical and computer-like, but that's the sort of OC brain I have!).

I work across every line and look at every pair. For each pair I look for any other pair that can be seen by the first pair that has one of the same numbers in it.

For example say <12> is in R1C2 - I look for a <1x> or a <2x> in row 1, column 2 and box 1.

Say I found a <23> in R4C2. Now I look for the "other pair". That is, I have a <12> and a <23> so now I'm looking for a <13> - that's the only other pair that is of interest.

I look for this other pair in the rows, columns and boxes occupied by the <12> and <23> pairs. If I find a <13> in any such row column or box occupied, then bingo - I have a potential XY wing.

I then identify which is the pivot and see what is "available" at the cells seen by both the pincers.

Cheers

[Asellus]

Keith,

Sheryl didn't clean up her candidates. For instance, the only cell in Row 6 that can be <8> is R6C6 because it is already determined. The <8> in R6C9 is no hidden single; it is an "invalid single."

Sheryl,

Once you have cleaned up the candidates on a grid, then you can search for XY Wings by looking at the "bivalue" cells (bivalue cells are cells that have only two possible candidates).

For instance, say you see a cell containing {57}. Check the cells that cell can "see", that is cells that are in the same Row, Column or Box. Look for another bivalue containing either a <5> or a <7>. Let's suppose you find a {58} cell in the same Row. You now have two of the three cells you need for a possible XY Wing.

The missing cell is a {78} cell. If either of the two cells can "see" a {78} cell, then you've found an XY Wing. If it is the {57} cell that sees the {78} cell, then {57} is the pivot and the {58} and {78} cells are capable of eliminating <8>s from their common "buddies" (cells "visible" to both of them). On the other hand, if it is the {58} cell that sees the {78}, then {58} is the pivot and the {57} and {78} cells are capable of eliminating <7>s from their common "buddies."

However, don't be discouraged if you find an XY Wing structure that doesn't have any candidates that it eliminates. We aren't always so lucky! But, it happens often enough that you will find it useful.

One more thing: if those three bivalue cells are all in the same "House" (i.e., a Row, Column or Box), then it is not an XY Wing. Instead, it is a "Locked Triple." In such a case, those three digits ({578} in my example) cannot occur anywhere else in that House; so you can eliminate any such candidates if they are there.

Hope you find this helpful.

PS: I previewing this, I see kragzy has posted much the same. However, sometimes it helps to have two different explanations of the same thing.

[sheryl]

asellus and kragzy,
well, thank you thank you thank you. this is very helpful and i am looking forward to trying it out on the next puzzle (later today actually). i am copying it and pasting it into a word document so i can keep it until it sinks in.

p.s. asellus, i do think i cleaned up my candidates because the grid did solve. i also thought i had already mentioned to keith that i thought he might be doing the wrong puzzle because candidates he found were already 'givens' in this puzzle and i was just giving him the candidates that i had found. however, if i gave him wrong info, please advise.

again, thank you both so much for helping me out. it feels good to have a clue!