The New Sudoku Players' Forum

by **blue** » Sun Dec 29, 2013 12:33 am

daj95376 wrote:Skyscraper???

With the two towers and the (weak) box link in B1 ... ?

by **daj95376** » Sun Dec 29, 2013 6:35 am

blue wrote:
daj95376 wrote:Skyscraper???

With the two towers and the (weak) box link in B1 ... ?

What I see is a Franken X-Wing w/2x remote fin cells:

Code: Select all: (Franken X-Wing (4)c15\r7b1) = 4r1c5 ... (remote fin linkage) || = 4r5c5 ... (chain leading to second X-Wing w/remote fin cell)

Chain leading to second X-Wing w/remote fin cell:

Code: Select all: (4-9)r5c5 = (9-8)r5c6 = (8-4)r8c6 = (??? X-Wing (4)r18\c24) || = 4r1c5 ... (remote fin linkage)

Skyscrapers are Sashimi X-Wing ... not Franken X-Wing.

You could drop both fish patterns and reduce your logic to a network.

Code: Select all: 4r3c1 = 4r7c1 - 4r7c5 = 4 r1c5 ... (see below) || = (4-9)r5c5 = (9-8)r5c6 = (8-4)r8c6 = 4r8c2 - 4r2c2 || = 4r8c4 - 4r1c4 = 4r1c5 ... (see below) (4-5)r1c5 = (5-6)r9c5 = 6r9c7 - (6=9)r8c7 - (9=4)r2c7 - 4r2c2

by **blue** » Sun Dec 29, 2013 8:50 am

Hi Danny,

daj95376 wrote:What I see is a Franken X-Wing w/2x remote fin cells:

Code: Select all
(Franken X-Wing (4)c15\r7b1) = 4r1c5 ... (remote fin linkage) || = 4r5c5 ... (chain leading to second X-Wing w/remote fin cell)

Chain leading to second X-Wing w/remote fin cell:

Code: Select all
(4-9)r5c5 = (9-8)r5c6 = (8-4)r8c6 = (??? X-Wing (4)r18\c24) || = 4r1c5 ... (remote fin linkage)

Right. Nothing wrong with that, or with your network diagram.
I was trying to avoid the (2x) "Kraken" feel that you get, showing things that way.
The AIC with pattern nodes, seemed more palatable.

daj95376 wrote:Skyscrapers are Sashimi X-Wing ... not Franken X-Wing.

When I want to think of them as fish, I only go as far as calling them finned X-wings.
If pressed, I would say they're "franken" or not (dealer's choice), depending on which tower candidate is designated as the fin.
I suppose they're Sashimi X-wings either way, although I've never been clear on the proper meaning of "Sashimi".

In your depiction above, both X-wings would be Sashimi ? (one Franken, one normal) ?

by **daj95376** » Sun Dec 29, 2013 12:43 pm

blue wrote:In your depiction above, both X-wings would be Sashimi ? (one Franken, one normal) ?

Although your "fish" concept works, I had a problem because traditional fin cells were missing to make the fish patterns stable.

I saw your initial pattern as a Kraken Franken X-Wing. However, without the Kraken cells, the Franken X-Wing degenerates. What's left is a Kraken Column [c5] on <4>. (the following is a repeat of an earlier post of mine)

Code: Select all: Kraken Cell: (4-5)r1c5 = (5-6)r9c5 = 6r9c7 - (6=9)r8c7 - (9=4)r2c7 - 4r2c2 Kraken Cell: (4-9)r5c5 = (9-8)r5c6 = (8-4)r8c6 = 4r8c2 - 4r2c2 4 r5c5 - 4r1c5 = 4r1c4 - 4 r8c4 / Franken X-Wing: 4 r7c5 - 4r7c1 = 4r3c1 - 4r2c2

Your second fish also degenerates because r1c5 can not be a Kraken cell when it's assumed that =4r5c5. I folded the logic into a secondary stream that merges with the first stream.

by **blue** » Mon Dec 30, 2013 12:11 am

daj95376 wrote:
blue wrote:In your depiction above, both X-wings would be Sashimi ? (one Franken, one normal) ?

Although your "fish" concept works, I had a problem because traditional fin cells were missing to make the fish patterns stable.

Body (not fin?) cells ?

daj95376 wrote:I saw your initial pattern as a Kraken Franken X-Wing. However, without the Kraken cells, the Franken X-Wing degenerates. What's left is a Kraken Column [c5] on <4>. (the following is a repeat of an earlier post of mine)

(...)

Your second fish also degenerates because r1c5 can not be a Kraken cell when it's assumed that =4r5c5. I folded the logic into a secondary stream that merges with the first stream.

I saw that ! I looked at that option too, before deciding on my first post.

Here's a nice diagram showing the (clearly degenerate) "fish".

Code: Select all: +-------------------------------------+ | 2nd fish | | 4r8c4 - 4r1c4 | | || || | | || 4r1c5 - (remote linkage) - | | || | | 4r8c2 - | | || | +-------------------------------------+ || 4r8c6 - 8r8c6 = (8-9)r5c6 = 9r5c5 - 4r5c5 || +------------------------------+ | || 1st fish | | 4r7c5 - 4r7c1 | | || || | | || 4r3c1 - | | || | | 4r1c5 - (remote linkage) - | | | +------------------------------+

This is another network approach, using the same AI streams, but handling the 4's differently:

Code: Select all: (4=9)r2c7 - (9=6)r8c7 - 6r9c7 = (6-5)r9c5 = (5-4)r1c5 = = 4r1c4 ----------------------------------------- \ \ 4r45c4 \ || \ 4r5c5 - 9r5c4 = (9-8)r5c6 = 8r8c6 \ || \ \ 4r45c6 --------------------------- 4r8c6 = 4r8c4 = 4r8c2 => -4r2c2

And the PMs for reference:

Code: Select all: +--------------+------------------+-------------+ | 3 9 8 | 45 45 6 | 1 2 7 | | 7 24 26 | 13 8 139 | 49 36 5 | | 46 1 5 | 237 29 2379 | 489 36 89 | +--------------+------------------+-------------+ | 9 8 7 | 346 1 34 | 2 5 46 | | 5 23 23 | 468 469 489 | 7 1 46 | | 1 6 4 | 25 7 25 | 38 9 38 | +--------------+------------------+-------------+ | 46 347 369 | 12467 246 1247 | 5 8 39 | | 2 45 69 | 458 3 458 | 69 7 1 | | 8 357 1 | 9 56 57 | 36 4 2 | +--------------+------------------+-------------+

by **JC Van Hay** » Mon Dec 30, 2013 3:02 am

A complementary view ... :idea:

After basics, r3c1=4 solves the puzzle while r3c1=6 leads to a contradiction.
As any elimination can be justified by using a Forbidding Matrix,
the shortest interpretation of the contradiction is given by the following chain of inferences :

Code: Select all: +---------------+---------------------+--------------+ | 3 9 8 | 5(4) (45) 6 | 1 2 7 | | 7 2-4 26 | 13 8 139 | (49) 36 5 | | 46 1 5 | 237 29 2379 | 489 36 89 | +---------------+---------------------+--------------+ | 9 8 7 | 346 1 34 | 2 5 46 | | 5 23 23 | 468 6(49) 4(89) | 7 1 46 | | 1 6 4 | 25 7 25 | 38 9 38 | +---------------+---------------------+--------------+ | 46 347 369 | 12467 26(4) 1247 | 5 8 39 | | 2 5(4) 69 | 58(4) 3 5(48) | (69) 7 1 | | 8 357 1 | 9 (56) 57 | 3(6) 4 2 | +---------------+---------------------+--------------+ 4r2c4 4r2c7=9r2c7 9r8c7=6r8c7 6r9c7=6r9c5 5r9c5=5r1c5 4r1c5=4r1c4 4r8c2=========================4r8c4=4r8c6 4r1c5=======4r7c5=4r5c5 8r8c6=======8r5c6 9r5c5=9r5c6

That 9-SIS FM (or nrczt-chain, here) can also be read in short as
r2c2=4->r2c7=9,r8c7=6,r9c5=6,r1c5=5,r1c4=4;r8c6=4=r5c5,r5c6=8; no place for a 9 in R5B5!

Reading the FM from the 7th row, one can write an "AIC"-like network :

Code: Select all: Chain [9] : 4r8c2=*[Skyscraper(4r1c5=4r1c4-4r8c4=*4r8c6)-8r8c6=(8-9)r5c6=9r5c5]-... ...-4r5c5=*[Kite(4r8c2=4r8c46-4r7c5=*4r1c5)-5r1c5=(5-6)r9c5=6r9c7-(6=9)r8c7-(9=4)r2c7] :=> [4r8c2==4r2c7]-4r2c2; ste

-------------------------------------------------------------------------------------------------------------------
If the puzzle is analyzed from B9 instead of B1,
the simpler following short solution is found, requiring only 7 SIS :

Code: Select all: +----------------+------------------+--------------+ | 3 9 8 | 45 45 6 | 1 2 7 | | 7 (24) (26) | 13 8 139 | (49) 36 5 | | 46 1 5 | 237 29 2379 | 489 36 89 | +----------------+------------------+--------------+ | 9 8 7 | 346 1 34 | 2 5 46 | | 5 23 23 | 468 469 489 | 7 1 46 | | 1 6 4 | 25 7 25 | 38 9 38 | +----------------+------------------+--------------+ | 46 347 369 | 12467 246 1247 | 5 8 39 | | 2 45 9-6 | 458 3 458 | (69) 7 1 | | 8 357 1 | 9 56 57 | 36 4 2 | +----------------+------------------+--------------+

#1. XYChain [4] : (6=9)r8c7-(9=4)r2c7-(4=2)r2c2-(2=6)r2c3 :=> -6r8c3; 10 Singles

Code: Select all: +-------------+-------------------+------------+ | 3 9 8 | 4 5 6 | 1 2 7 | | 7 24 26 | 13 8 139 | 49 36 5 | | 46 1 5 | 237 29 2379 | 49 36 8 | +-------------+-------------------+------------+ | 9 8 7 | 36 1 34 | 2 5 46 | | 5 23 23 | 68 (49) 4(89) | 7 1 46 | | 1 6 4 | 25 7 25 | 8 9 3 | +-------------+-------------------+------------+ | 46 347 36 | 127 2(4) 1247 | 5 8 9 | | 2 45 9 | 58 3 5-4(8) | 6 7 1 | | 8 57 1 | 9 6 57 | 3 4 2 | +-------------+-------------------+------------+

#2. Wing[8r8c6=(8-9)r5c6=(9-4)r5c5=4r7c5]-4r8c6; ste

by **daj95376** » Tue Dec 31, 2013 9:16 pm

blue wrote:
daj95376 wrote:
blue wrote:In your depiction above, both X-wings would be Sashimi ? (one Franken, one normal) ?

Although your "fish" concept works, I had a problem because traditional fin cells were missing to make the fish patterns stable.

Body (not fin?) cells ?

Sorry, but this really isn't an issue. One of my biases about Fish came into play and blurred my objectivity. I was expecting an exo-fin cell to be present along with any remote/Kraken fin cells. Without an exo-fin cell, many fish will degenerate when the remote/Kraken fin cells are treated as being false. This isn't technically "a problem", but degeneration is how I often differentiate a Fish with remote/Kraken cells from a Kraken Unit scenario. That's why I transformed your solution into a Kraken Column on [c5].

With remote/Kraken fin cells considered false on your first fish, r2c5 needs to be an exo-fin cell to prevent degeneration.

Code: Select all: X * * | . // . | . . . X ** ** | . # . | . . . X * * | . / . | . . . ---------+---------+--------- / . . | . / . | . . . / . . | . // . | . . . / . . | . / . | . . . ---------+---------+--------- X * * | * X * | * * * / . . | . / . | . . . / . . | . / . | . . . Fig 2D: cc\rb (morphed RonK exemplar)

Otherwise, we get:

Code: Select all: X * * | . // . | . . . X * * | . / . | . . . X * * | . / . | . . . ---------+---------+--------- / . . | . / . | . . . / . . | . // . | . . . / . . | . / . | . . . ---------+---------+--------- X * * | * X * | * * * / . . | . / . | . . . / . . | . / . | . . . Degeneration when remote/Kraken fin cells are considered false (//) (X): r7c5 - r7c1 = r3c1 - r2c2

A similar situation occurs for your second fish.

I'm sorry for the confusion that I created !!!

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