Combinations of 3 or 4 strong and weak inferences

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Combinations of 3 or 4 strong and weak inferences

Postby 999_Springs » Sun Oct 10, 2010 10:30 pm

Old thread from the players' forum with some extra stuff added on. I've got some more stuff about this which I'll post here in a few days when I have time.

Yes, I made up some silly names. Just because I got bored. I doubt they'll actually ever be used but it'd be really funny so I encourage you to use the new names as often as possible even if it makes yourself sound weird.

3 weak and 3 strong inferences - continuous loop

("errr" has been renamed "Zap")
Code: Select all
. . *-----1-----* . .
. . # | . . . | # # .
. . # | . . . | # # *
------+-------+-----|
. . # | . . . | . . |
. . # | . . . | . . 1
. . # | . . . | . . |
------+-------+-----|
. . # | . . . | # # *
. . # | . . . | # # .
. . *------1------* .
1. Unfinned mutant swordfish
# =/= 1



. . # | . . . | . . .
. . # | . . . | . . .
/ / 12| / / / | * / /
------+-------+-|----
. . # | . . . | | . .
. . # | . . . | 1 . .
. . # | . . . | | . .
------+-------+-|----
. . *-----2-----*@. .
. . # | . . . | . . .
. . # | . . . | . . .
2. Zap
/ =/= 1
# =/= 2
@ = 12


4 weak and 3 strong inferences - discontinuous loop

(All have been named before)
Code: Select all
. . . | . . . | . . .
. . . | . . . | . . .
. . 12| . . . | 13. .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . 23| . . . | # . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
1. XY-wing
# =/= 3



. . . | . . . | . . .
. . *-----1-----* . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . 12| . . . | # . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . # | . . . | 12. .
2. W-wing
# =/= 2



. . . | . . . | . . .
. . *-----1-----* . .
. . | | . . . | . . .
----2-+-------+------
. . | | . . . | . . .
. . * | . . . | # . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | 12. .
3. Generalised M-wing
# =/= 2



. . . | . . . | . . .
. . . | . . . | . . .
. . *------1------* .
----|-+-------+---|--
. . 2 | . . . | . 3 .
. . | | . . . | . | .
. . *#| . . . | . *@.
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
4. Hybrid Wing 1
# =/= 3
@ =/= 2



. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
*-----2-----* | . . .
| . . | . . . | . . .
1 . . | . . . | . . .
|-----+-------+------
*#. . | . . 23| . . .
. . . | . . . | . . .
. . . | . . . | . . .
5. Hybrid Wing 2
# =/= 3



. . . | . . . | . . .
. * . | . . 12| . . .
. | . | . . . | . . .
--|---+-------+------
. | . | . . . | . . .
. 1 . | . . . | . . .
. | . | . . . | . . .
--|---+-------+------
. | . | . . . | . . .
. *#. | . . 23| . . .
. . . | . . . | . . .
6. Hybrid Wing 3
# =/= 3



. . *---1---*#| . . .
. . . | . . . | . . .
. . *---2---*@| . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . 12| . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
7. Split Wing
# =/= 2
@ =/= 1



. . . | . . . | . . .
. *---1---*---2---* .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. *-------1-------*#.
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
8. I-Never-Saw-A-Purple-Cow-I-Hope-I-Never-See-One-But-I-Can-Tell-You-This-Right-Now-I'd-Rather-See-Than-Be-One
# =/= 2



. . . | . . . | . . .
. # # | . . . | . . *
* . . | . . . | # # |
|-----+-------+-----|
| . . | . . . | . . |
1 . . | . . . | . . 1
| . . | . . . | . . |
|-----+-------+-----|
| . . | . . . | . . *
* . . | . . . | . . .
. . *------1------* .
9. 3 strong links
# =/= 1


3 weak and 4 strong inferences - discontinuous loop

All of these are just "direct" versions of the 4-weak 3-strong ones so they're not included here. By "direct" I mean it reveals a single immediately afterward.
Code: Select all
(You could rent out this space for adverts)


4 weak and 4 strong inferences - continuous loop

(I'm 95% sure this is complete. Tell me if I missed one. I haven't put the eliminations in for lack of bothered-ness.)
Code: Select all
. . . | . . . | . . .
. . . | . . . | . . .
. . 12| 13. . | . . .
------+-------+------
. . 24| 34. . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
1. XY-Ring



*---------1---------*
| . . | . . . | . . |
| . . | . . . | . . |
|-----+-------+-----|
| . . | . . . | . . |
2 . . | . . . | . . 3
| . . | . . . | . . |
|-----+-------+-----|
| . . | . . . | . . |
| . . | . . . | . . |
*---------4---------*
2. Strong Ring



. . . | . . . | . . .
. *------2------*. .
. | . | . . . | . . .
--|---+-------+------
. | . | . . . | . . .
. 1 . | *---2---* . .
. | . | | . . | . . .
--|---+-1-----+------
. | . | | . . | . . .
. * . | * . . | . . .
. . . | . . . | . . .
3. Blood-red eyes and tentacles



. . 12| . . . | . . *
. . . | . . . | . . |
. . . | . . . | . . 2
------+-------+-----|
. . . | 12. . | . . *
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . *-1-* . . | . . .
4. Rotten cake made out of wood



*-----3-----* | . . .
| . . | . . . | . . .
| . . | . . . | . . .
1-----+-------+------
| . . | . . 23| . . .
| . . | . . . | . . .
*---2---* . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
5. [Insert Name Here]



. . . | . ./* | . . .
. . . | . 3 | | . . .
. . 13| */. | | . . .
------+-----2-+------
. . . | . . | | . . .
. . . | . . | | . . .
. . 12| . . * | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
6. IKEA Sucks



. . . | . . . | . . .
. . . | * . 12| . . .
. . . | | . . | . . .
------+-|-----+------
. . . | | . . | . . .
. . . | 1 . *---2---*
. . . | | . . | . . .
------+-|-----+------
. . . | | . . | . . .
. . . | *-----2-----*
. . . | . . . | . . .
7. Cheese



* . . | . 12. | . . .
| . . | . . 23| . . .
| . . | . . . | . . .
|-----+-------+------
1 . . | . . . | . . .
| . . | . . . | . . .
| . . | . . . | . . .
|-----+-------+------
* . . | . . 13| . . .
. . . | . . . | . . .
. . . | . . . | . . .
8. This is the song that doesn't end,/ Yes it goes on and on my friend,/ Some people started singing it, not knowing what it was,/ And they continued singing it forever just because...



. *--1--*\. . | . . .
. . . | . 2 . | . . .
. . . | . .\* | . . .
------+-----|-+------
. . . | . . 3 | . . .
. . . | . . | | . . .
. *----1----* | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
9. Don't eat this.



. *------1------* . .
. . . | . . . | . . *
* . . | . . . | . . |
|-----+-------+-----|
| . . | . . . | . . |
1 . . | . . . | . . 1
| . . | . . . | . . |
|-----+-------+-----|
| . . | . . . | . . *
* . . | . . . | . . .
. . *------1------* .
10. Unfinned Mutant Jellyfish


As said above, I'll add some more stuff here in a few days when I have the time.

[Edit: Added 3 strong links. How did I forget that!?]
Last edited by 999_Springs on Fri Oct 22, 2010 7:32 pm, edited 1 time in total.
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Re: Combinations of 3 or 4 strong and weak inferences

Postby AR4793 » Sun Oct 10, 2010 11:32 pm

AR4793 wrote:This isn't me! :lol:


I rightfully got handed my head for trying to coin some terms in the Sudopedia. :oops:

Voting is an interesting way to try to form a majority opinion.

Now I'm having a senior moment. Just what was an out of the water inverse green flying bat winged pink swordfish with fins... ? ?

Regards,
Herb
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Re: Combinations of 3 or 4 strong and weak inferences

Postby daj95376 » Mon Oct 11, 2010 4:07 am

I'll need to think over your naming suggestions. In the meantime, here are a few names that are being used in the DailySudoku forum. The M-Wing is the generalized form.

Code: Select all
M-Wing:      (A=B)   -  B  =   (B-A)   =   A

W-Wing:      (A=B)   -  B  =  B  -   (B=A)

S-Wing:     A  =  A  -   (A=B)   -  B  =   B   {1st A and last B in the same house}

L-Wing:     A  =  A  -  A  = (A  -  B) =   B   {1st A and last B in the same house}
(reverse)   B  = (B  -  A) =  A  -  A  =   A   {1st B and last A in the same house}
___________________________________________________________________________________

Obviously, they all use two candidates and three strong inferences.
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Re: Combinations of 3 or 4 strong and weak inferences

Postby StrmCkr » Mon Oct 11, 2010 4:37 am

Zap
was already named as well its a a M-ring
Some do, some teach, the rest look it up.
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Re: Combinations of 3 or 4 strong and weak inferences

Postby 999_Springs » Fri Oct 22, 2010 7:29 pm

Poll ended 2-1 in my favour. Therefore, by majority vote, I declare these names to be the official nomenclature for all occurrences of combinations of 3 or 4 strong and weak inferences for forevermore. Woe betide those who question or deny their eternal glory.

Anyway, moving on.

"Inversion"

Well I didn't know what else to call this, but whatever. I don't know if this has been done before, or whether it has any use whatsoever (I can't find any), but here goes.

To invert a pattern of weak and strong links, you do the following.
- Where every strong link was, replace it with a weak link.
- Where every weak link was, replace it with a strong link.
- If the loop was originally discontinuous, the elimination becomes a placement.
- If the loop was originally continuous, the eliminations... They do something. I haven't worked this out yet.

If you do this you get another valid pattern. For example: the Unfinned Mutant Swordfish 1r1c37 r37c9 r9c38 inverts to another Unfinned Mutant Swordfish 1r19c3 r1c7r3c9 r7c9r9c8. Not sure how you'd prove that you'd always get another valid pattern.

If you invert a pattern twice you get what you started with. That's obvious.

Results:

3 weak 3 strong case:
A 3 weak 3 strong pattern will invert to another one of the same kind.
Unfinned Mutant Swordfish inverts to itself.
Zap (aka M-Ring) inverts to itself.

4 weak 3 strong case:
A 4 weak 3 strong pattern will invert to a 4 strong 3 weak pattern. It turns out that the extra strong link serves no purpose than to make the pattern "direct" (see the OP for definition) so you can just take the surplus strong link out and you get another pattern of 4 weak 3 strong links. But there is occasionally more than 1 way of doing this for each pattern.
XY-Wing inverts to a direct Hybrid Wing 1.
W-Wing inverts to a direct I-Never-Saw-A-Purple-Cow-I-Hope-I-Never-See-One-But-I-Can-Tell-You-This-Right-Now-I'd-Rather-See-Than-Be-One.
M-wing inverts to a direct Split Wing.
Hybrid Wing 1 inverts to either a direct XY-Wing or a direct Hybrid Wing 3 depending on which strong link you remove.
Hybrid Wing 2 inverts to a direct version of itself.
Hybrid Wing 3 inverts to a direct Hybrid Wing 1.
Split Wing inverts to a direct M-Wing.
I-Never-Saw-A-Purple-Cow-I-Hope-I-Never-See-One-But-I-Can-Tell-You-This-Right-Now-I'd-Rather-See-Than-Be-One inverts to a direct W-Wing.
3 strong links inverts to a direct version of itself.

4 weak 4 strong case:
A 4 weak 4 strong pattern will invert to another one of the same kind.
XY-Ring and Strong Ring invert to each other.
Blood-red eyes and tentacles and Rotten cake made out of wood invert to each other.
[Insert Name Here] and IKEA Sucks invert to each other.
Cheese inverts to itself.
This is the song that doesn't end,/ Yes it goes on and on my friend,/ Some people started singing it, not knowing what it was,/ And they continued singing it forever just because... and Don't eat this. invert to each other.
Unfinned Mutant Jellyfish inverts to itself.

Conclusion: I see absolutely no practical use for this whatsoever. Maybe, just maybe, I've touched upon an obscure sub-branch of graph theory that is vaguely related to something useful. But probably not.
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Re: Combinations of 3 or 4 strong and weak inferences

Postby 999_Springs » Sun Oct 31, 2010 10:21 pm

Oh come on. At least someone tell me whether this is new or not.

@Daj95376 Bud has been using my alternative name Purple Cow instead of the L-wing on the dailysudoku forum. Here's the relevant post. (Which I'm sure has been edited. It had only one example in it last week.)
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Re: Combinations of 3 or 4 strong and weak inferences

Postby daj95376 » Mon Nov 01, 2010 12:04 am

999_Springs wrote:Oh come on. At least someone tell me whether this is new or not.

@Daj95376 Bud has been using my alternative name Purple Cow instead of the L-wing on the dailysudoku forum. Here's the relevant post. (Which I'm sure has been edited. It had only one example in it last week.)

The post now has two examples labeled as extended Purple Cow.

I don't recall paying much (if any) attention to the post. Most of my work on identifying L-Wings has been recent. More recent than the original post by Bud. In addition, my solver doesn't flag extended Wings. I have to manually catch them in a generic list of chains. I can do it, but I seldom do so.

Finally, the S/L-Wings were barely accepted as reasonable companions to the 3-Strong/2-Weak M/W-Wings. Few in that forum seem interested in using the S/L-Wings.

Regards, Danny
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