The New Sudoku Players' Forum

[StrmCkr]

xy-wing is an als-xz function as well, just to chime in

xyz-wing:
the wing has 1 extra digit attached at the pivot cell, still functions identical to the xy-wing, construction restricts it to being a box + row/col intersection where the 3rd digit set as true is the elimination and wont chain anywhere, that way the z digit is solved in both end points and pivot as truth, anything that sees all 3 truths must be false.

a spit wing
the corrected notation:

S-Wing: (X)a = (X)b - (X=Y)c - (Y)d = (Y)e "a" and "e" in same unit; a<>Y, e<>X
but not in the same cell -- else M-Ring

it starts with a bivalve in the middle, and which has candidate X,Y

candidates X and Y go off in separate directions via strong or grouped links
x end point sees the end point of y.

that way when the bivalve solves as X or Y the end points result in : X can be x but never Y, and Y can be y but never x.
{discontinuous nice loop}

Code: Select all

+------------+---------+-----------------+
| .  .     . | .  .  . | .      .      . |
| .   A    . | .  .  . | -B A   .      . |
| .  .     . | .  .  . | .      -A B   . |
+------------+---------+-----------------+
| .  .     . | .  .  . | .      .      . |
| .   AB   . | .  .  . | .       B     . |
| .  .     . | .  .  . | .      .      . |
+------------+---------+-----------------+
| .  .     . | .  .  . | .      .      . |
| .  .     . | .  .  . | .      .      . |
| .  .     . | .  .  . | .      .      . |
+------------+---------+-----------------+
note:
Col 7 is strong links for B { 2 spots left which are marked}
Row 2 is strong links for A { 2 spots left which are marked}



[SpAce]

xy-wing is an als-xz function as well, just to chime in

Yes, it can be seen that way too. It's also an XY-Chain of length three with three strong links, and as such a "wing" by that particular definition. That's not true for XYZ-Wing if you look at it as an AIC. It only has two nodes and two strong links no matter how you look at it.

xyz-wing: the wing has 1 extra digit attached at the pivot cell, still functions identical to the xy-wing

I don't see its function identical to the XY-Wing. The latter (when viewed as an XY-Chain) is a simple chain with two one-cell end-points and three nodes total. When the XYZ-Wing is seen as a chain, one of the ends is a two-cell (almost-)naked-pair, and it only has two nodes. That's why my earlier point was that the XYZ description as a three-node AIC seemed wrong.

, construction restricts it to being a box + row/col intersection where the 3rd digit set as true is the elimination and wont chain anywhere, that way the z digit is solved in both end points and pivot as truth, anything that sees all 3 truths must be false.

That's the third way of seeing the XYZ-Wing: as a forcing net with three (very short) branches emanating from the pivot (the XY-Wing is also a forcing chain if you start at the pivot, but it only has two branches). I prefer the AIC view to that or the ALS-XZ, but it's just a matter of taste.

a spit wing

the corrected notation:

S-Wing: (X)a = (X)b - (X=Y)c - (Y)d = (Y)e "a" and "e" in same unit; a<>Y, e<>X
but not in the same cell -- else M-Ring

Thanks, that was helpful! Now I think I get it.

it starts with a bivalve in the middle, and which has candidate X,Y
candidates X and Y go off in separate directions via strong or grouped links

That's the forcing chain point of view of it. Again, I rather see it as an AIC like everything else.

x end point sees the end point of y.
that way when the bivalve solves as X or Y the end points result in : X can be x but never Y, and Y can be y but never x.

So it's a special case of Hodoku AIC Type 2 (different digits at the ends which see each other), like the L-Wing and H-Wing as well. The rest are AIC Type 1 (the same digit at the ends).

The mystery of wings and rings mostly solved, I think. Easy enough now that I can place them in the correct baskets. Like I've said, there's no real need to memorize all of these wing types as long as one understands the fundamentals of AICs. Recognizing such recurring patterns can of course help in spotting those chains faster, however.

[StrmCkr]

Thanks, that was helpful! Now I think I get it.

it starts with a bivalve in the middle, and which has candidate X,Y
candidates X and Y go off in separate directions via strong or grouped links

That's the forcing chain point of view of it. Again, I rather see it as an AIC like everything else.

well, that's the easiest way to explain it quickly as you asked for some explanation on the split wing I developed
the aic notation is:

S-Wing: (X)a = (X)b - (X=Y)c - (Y)d = (Y)e "a" and "e" in same unit; a<>Y, e<>X
but not in the same cell -- else M-Ring

i do agree that the fundamentals is all you really need, most of the naming is just tagged to the appropriate size when listing it out but even that can be dropped if you choose.

[SpAce]

The problem with so many names that are coined is that they are not picked up by the forum's search engine; for example, try searching for M-Wing and X-Wing. Innovators would be well advised to consider this.

This is true, and it's very annoying. Does anyone know what the problem is? Is it the dash? Any work-around available? I've tried removing the dash, and putting quotation marks around, but none of it helps. It's better to bookmark any interesting pages about wings if one wants to find them later.

[SpAce]

One notation question. All of these "remote pair like" wings are normal AICs and easy to notate, but how do you notate an actual Remote Pair chain? It really has two intertwined AICs (XY-Chains) which are easy to notate separately, but we obviously want to use it as one move. Do you just show one chain and call it Remote Pair to justify both elimination digits?

[JasonLion]

the forum's native search engine is terrible. You are almost always better off using -site: searches at Google.