POM Analysis of the X-Wing: The Filet-O-Fish Rule

Advanced methods and approaches for solving Sudoku puzzles

Postby PhilC » Fri Jan 20, 2006 7:06 pm

Hey, I'm new to this forum and I'm trying to learn this filet-o-fish technique. Please tell me if this is correct:

Code: Select all
+----------+-----------+-----------+
| .  2  2  |  .  2  .  |  2 -2  .  |
| .  .  2  |  .  2  2  |  .  .  2  |
| . *2  .  |  . #2 #2  |  . *2 #2  |
+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  .  .  |
| .  .  2  |  .  .  .  |  2  .  .  |
| . *2  .  |  .  .  .  |  . *2  .  |
+----------+-----------+-----------+
| .  .  .  |  .  2  2  |  .  2  2  |
| .  .  .  |  .  2  2  |  2  .  2  |
| .  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+
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Postby ronk » Fri Jan 20, 2006 7:38 pm

PhilC wrote:Please tell me if this is correct:

Code: Select all
+----------+-----------+-----------+
| .  2  2  |  .  2  .  |  2 -2  .  |
| .  .  2  |  .  2  2  |  .  .  2  |
| . *2  .  |  . #2 #2  |  . *2 #2  |
+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  .  .  |
| .  .  2  |  .  .  .  |  2  .  .  |
| . *2  .  |  .  .  .  |  . *2  .  |
+----------+-----------+-----------+
| .  .  .  |  .  2  2  |  .  2  2  |
| .  .  .  |  .  2  2  |  2  .  2  |
| .  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+

IMO the elimination cannot be r1c8#2 ... because it cannot "see" all the fins. Indeed, I don't think any eliminations are possible when three fins exist. However, if there were no fins at r3c5 and r3c6, your elimination would be correct.

But I'm a filet-o-fish newbie too, so use salt generously, Ron
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Postby Myth Jellies » Sat Jan 21, 2006 9:04 am

Ronk has it nailed concerning the need for all of your fins to be in the same box so they can be seen by the deletion cell. I think the following pattern shows that you can have up to 4 cells in the fin. Probably not very likely in nature though.

Code: Select all
+----------+-----------+-----------+
| .  2  2  |  2  2  2  | -2- 2  2  |
| .  . *2  | *2 *2  .  | *2 #2 #2  |
| .  . *2  | *2 *2  .  | *2 #2 #2  |
+----------+-----------+-----------+
| .  2  2  |  2  2  2  |  2  2  2  |
| .  . *2  | *2 *2  .  | *2  .  .  |
| .  2  2  |  2  2  2  |  2  2  2  |
+----------+-----------+-----------+
| .  . *.  | *2 *2  .  | *2  .  .  |
| .  .  .  |  2  2  2  |  2  2  2  |
| 2  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+


The x-cycle groupers can have a little fun with this one:) .
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Postby ronk » Sat Jan 21, 2006 1:26 pm

Myth Jellies wrote:The x-cycle groupers can have a little fun with this one:) .

Funny double entendre. You must love to fish or love to eat fish or both ... assuming you're not part fish, of course.
:D:D
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Postby Carcul » Sat Jan 21, 2006 3:24 pm

Myth Jellies wrote:The x-cycle groupers can have a little fun with this one


Translating the deduction r1c7<>2 to nice loop language requires indeed some imagination. Here is a sugestion:

[r1c7](-2-[r1c6])(-2-[r78c7]=2=[r8c89]-2-[r8c6])-2-[r1c23]=2=[r23c3]-2-[r456c3]=2=[X-Wing:r46c26]-2-[r4c789|r6c789]=2=[r5c7]-2-[r1c7], => r1c7<>2.

Regards, Carcul
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Postby ronk » Sat Jan 21, 2006 4:29 pm

Carcul wrote:
Myth Jellies wrote:The x-cycle groupers can have a little fun with this one


Translating the deduction r1c7<>2 to nice loop language requires indeed some imagination. Here is a sugestion:

[r1c7](-2-[r1c6])(-2-[r78c7]=2=[r8c89]-2-[r8c6])-2-[r1c23]=2=[r23c3]-2-[r456c3]=2=[X-Wing:r46c26]-2-[r4c789|r6c789]=2=[r5c7]-2-[r1c7], => r1c7<>2.

Congratulations! I don't expect there are many people that can understand that, let alone come up with it. For example, I don't understand the x-wing part.

But where "simple" overlaps exist:
1. Why did you choose the expression "[r1c7]-2-[r1c23]=2=[r23c3] ..."
... instead of "[r1c7]-2-[r1c2]=2=[r123c3] ..."?

2. Similarly, why did you choose the expression "[r1c7]-2-[r78c7]=2=[r8c89]-2-[r8c6] ..."
... instead of "[r1c7]-2-[r7c7]=2=[r8c789]-2-[r8c6] ..."?

Regards, Ron
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Postby Carcul » Sat Jan 21, 2006 4:55 pm

Hi Ronk.

Ronk wrote:1. Why did you choose the expression "[r1c7]-2-[r1c23]=2=[r23c3] ..."
... instead of "[r1c7]-2-[r1c2]=2=[r123c3] ..."?


Both notations are equivalent, its just a question of "taste".

Ronk wrote:2. Similarly, why did you choose the expression "[r1c7]-2-[r78c7]=2=[r8c89]-2-[r8c6] ..."
... instead of "[r1c7]-2-[r7c7]=2=[r8c789]-2-[r8c6] ..."?


Same here.

Ronk wrote:For example, I don't understand the x-wing part.


If r1c7=2:

(a) r1c6<>2
(b) r78c7<>2 => one of r8c89=2 => r8c6<>2.
(c) r1c23<>2 => one of r23c3=2 => r456c3<>2

Now we have a X-Wing in cells r4c2/r4c6/r6c2/r6c6 that eliminates all "2s" in box 6 except r5c7 - but r1c7 is already "2", which is a contradiction, so r1c7<>2.

Regards, Carcul
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Postby Myth Jellies » Sat Jan 21, 2006 8:00 pm

ronk wrote:Myth Jellies wrote:
The x-cycle groupers can have a little fun with this one .

Funny double entendre. You must love to fish or love to eat fish or both ... assuming you're not part fish, of course.


I was hoping someone would catch that [grouper = large sea bass]. I can only claim partial credit though, since I didn't realize what I had done until after I had written it down. Actually, I am none of those. Mark me down as an aquarium buff. Got the annual pass to the Aquarium of the Pacific, and are hoping to come out your way to catch the new whale shark exhibit in the ATL.

Carcul wrote:Translating the deduction r1c7<>2 to nice loop language requires indeed some imagination. Here is a sugestion:

[r1c7](-2-[r1c6])(-2-[r78c7]=2=[r8c89]-2-[r8c6])-2-[r1c23]=2=[r23c3]-2-[r456c3]=2=[X-Wing:r46c26]-2-[r4c789|r6c789]=2=[r5c7]-2-[r1c7], => r1c7<>2.


I'll agree with you on that. You must either be a groupy looper or a loopy grouper to come up with this:D . I need a picture...

Code: Select all
+----------------+----------------+----------------+
| .    2b"  2b"  | 2    2    2bcd | 2A   2    2    |
| .    .    2c"  | 2    2    .    | 2    2    2    |
| .    .    2c"  | 2    2    .    | 2    2    2    |
+----------------+-----------------+---------------+
| .    2X   2d"d | 2    2    2X   | 2B   2B   2B   |
| .    .    2d"d | 2    2    .    | 2C   .    .    |
| .    2X   2d"d | 2    2    2X   | 2B   2B   2B   |
+----------------+----------------+----------------+
| .    .    .    | 2    2    .    | 2b'  .    .    |
| .    .    .    | 2    2    2d'cd| 2b'  2c'  2c'  |
| 2    .    .    | .    .    .    | .    .    .    |
+----------------+----------------+----------------+


...so if I understand this correctly, it goes something like...
Code: Select all
  b' = c' - d'++
 /             c++++
A --------- b+++   d = X - B = C - A
 \                 +
  b" = c" - d"++++++

...where c is a composite of b and d', and d is a composite of c and d". I think I understand it, but don't ask me to ever look for it, I can just barely draw the thing:)
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Postby ronk » Sun Jan 22, 2006 3:05 am

Carcul wrote:
Ronk wrote:For example, I don't understand the x-wing part.

If r1c7=2:

(a) r1c6<>2
(b) r78c7<>2 => one of r8c89=2 => r8c6<>2.
(c) r1c23<>2 => one of r23c3=2 => r456c3<>2

Now we have a X-Wing in cells r4c2/r4c6/r6c2/r6c6 that eliminates all "2s" in box 6 except r5c7 - but r1c7 is already "2", which is a contradiction, so r1c7<>2.

Thanks, but why is col 3 involved. Isn't r1c6<>2, r8c6<>2, and r1c2<>2 sufficient to "create" the x-wing?
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Postby Jeff » Sun Jan 22, 2006 4:00 am

Myth Jellies wrote:...so if I understand this correctly, it goes something like...
Code: Select all
  b' = c' - d'++
 /             c++++
A --------- b+++   d = X - B = C - A
 \                 +
  b" = c" - d"++++++

Hi Carcul and MJ, This grouper is very good catch indeed. It will take some time before any fishermen can break this record.:D

Judging from the diagram which does look like a fish, the almost x-wing actually has 3 out of the 5 fins of a fish. According to their approximate locations, they are:

b" = pectoral fin
b = pelvic fin
d' = dorsal fin

Here is a reference for the body of a fish:

Most fishes are mobile underwater predators and their bodies have adapted accordingly. For most fishes, this means a streamlined body that can move swiftly through the water. A typical fish has a fusiform shape, pointed to penetrate the water in front and tapered to the rear, finished with a broadly expanded tail fin that provides propulsive force. Additional fins on the body’s midline, the dorsal fin and anal fin, and paired pelvic fins act as stabilizers to prevent rolling from side to side. Paired pectoral fins provide fine movements, add forward thrust, or, together with the pelvic fins, serve as brakes.:D
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Postby Myth Jellies » Sun Jan 22, 2006 4:30 am

Jeff, that's just ichthy!

[edit: sheesh I need to learn how to spell]
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Postby ronk » Sun Jan 22, 2006 1:10 pm

Jeff wrote:Here is a reference for the body of a fish:

Here is a picture (tail fin <=> caudal fin)::D:D

Image
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Postby tarek » Wed Jan 25, 2006 1:14 pm

Just a quick question,

If the FINNED vertex of a (Finned fish) is on its own (only veretx in the line of elimination), would it be correct to say that any of the Fin Cells can serve as a vertex point & therefore eliminate along extra lines corresponding to the number of cells constituting the fin ? (up to 3 simultaneous FINNED fishes !!!)

Code: Select all
+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  .  1  |
| . *1  .  | *1  .  .  |  . -1  .  |
| .  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+
| . *1  .  |  .  .  .  |  .  .  .  |
| .  .  .  | *1  .  .  | *1  .  .  |
| .  .  1  |  .  .  .  |  .  .  1  |
+----------+-----------+-----------+
| .  . -1  |  .  .  .  |#*1  .  .  |
| .  .  .  |  . -1  .  |#*1  .  .  |
|-1  .  .  |  .  . -1  |#*1  .  .  |
+----------+-----------+-----------+


The above leads to a contradiction, where did I go wrong ???

Does this mean that the rule only applies when the Fin belongs to a GROUPED vertex (there would be no problem with an x-wing as the veteces are already grouped) ???!!!!

Thanx

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Postby ronk » Wed Jan 25, 2006 4:39 pm

tarek wrote:
Code: Select all
+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  .  1  |
| . *1  .  | *1  .  .  |  . -1  .  |
| .  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+
| . *1  .  |  .  .  .  |  .  .  .  |
| .  .  .  | *1  .  .  | *1  .  .  |
| .  .  1  |  .  .  .  |  .  .  1  |
+----------+-----------+-----------+
| .  . -1  |  .  .  .  |#*1  .  .  |
| .  .  .  |  . -1  .  |#*1  .  .  |
|-1  .  .  |  .  . -1  |#*1  .  .  |
+----------+-----------+-----------+


The above leads to a contradiction, where did I go wrong ???

If you consider the "potential swordfish" to be in rows, then the fin cell (#) and elimination cells (-)("eye") would be:
Code: Select all
+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  .  1  |
| . *1  .  | *1  .  .  |  * #1  .  |
| .  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+
| . *1  .  |  *  .  .  |  *  .  .  |
| .  *  .  | *1  .  .  | *1  .  .  |
| .  .  1  |  .  .  .  |  .  .  1  |
+----------+-----------+-----------+
| .  .  1  |  .  .  .  | -1  .  .  |
| .  .  .  |  .  1  .  | -1  .  .  |
| 1  .  .  |  .  .  1  | -1  .  .  |
+----------+-----------+-----------+

... but there are no eliminations possible because the eyes don't "see" the fin. If you consider the potential swordfish to be in cols, then the eye(s) and fin(s) are swapped, but the eye still doesn't see the fins.
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Postby tarek » Wed Jan 25, 2006 5:07 pm

Thanx ronk,

As you mentioned there is an ALMOST X-wing with the elimination cells you mentioned.

I made a mistake in my post. This is actually how it should look like...

Code: Select all
+----------+-----------+-----------+
| 1  .  .  |  .  .  1  |  .  1  1  |
| . *1  .  | *1  .  .  |  .  .  .  |
| .  .  .  |  .  .  .  |  .  1  .  |
+----------+-----------+-----------+
| . *1  .  | *1  .  .  | *1  .  .  |
| .  .  .  |  .  1  .  |  .  1  .  |
| .  .  1  |  .  .  .  |  .  .  1  |
+----------+-----------+-----------+
| .  . -1  |  .  .  .  |#*1  . +1  |
| .  .  .  |  . -1  .  |#*1  . +1  |
|-1  .  .  |  .  . -1  |#*1  . +1  |
+----------+-----------+-----------+




what about the The swordfish in my example with The final vertix being ANY of the cells marked with "*" in box 9, would the other 2 constitute a fin ?????

Is it because there is an x-wing that the above arrangement would be invalid.
[Edited] I've added to the example, would the eliminations marked with + be valid
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