Almosting - Try to generialize how ALS works.

Advanced methods and approaches for solving Sudoku puzzles

Almosting - Try to generialize how ALS works.

Postby Gerra » Wed May 21, 2008 9:54 am

As I scanned my table for Almost Locked Sets, I asked myself: Why "Almosting" only the subsets? In this partial fiction-table I tried to imagine some possible cases of Almost patterns.

There are four different ways to attack candidate 6 (marked red) in r5c6. The eliminations are chained up with weak links provided by 4 (marked green) in box 5. Any of the four four in box 5 is true, the three others is forced to be false. Then comes the Almosts.

Image

-If the candidate 4 in r6c6 is false, then the classic Almost Locked Set (orange candidates) in c6 kills the red 6.

-If the candidate 4 in r4c5 is false, then trough the inference chain of 4 (ends up in the bivalue cell in r3c9), the candidate 6 (marked cyan) in r3c9 cannot be true, so the Almost X-Wing (r15c29, marked cyan) become repaired, kills the red 6.

-If the candidate 4 in r4c6 is false, then it repairs the Almost XYZ-wing (marked yellow) killing the red 6.

-If the candidate 4 in r4c4 is false, trough the short inference chain (ends up with the bivalue cell in r2c4), the 6 in r2c4 cannot be true, what repairs the Almost X-Chain (marked purple), what kills the red 6.

Almost everything can be Almosted, I suppose, and these Almost patterns can be chained up with anything.
Last edited by Gerra on Wed May 21, 2008 7:32 am, edited 4 times in total.
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Postby tarek » Wed May 21, 2008 10:23 am

Hi Gerra,

All these ALMOST patterns will provide Sticky ends.... these would then fit compatible sticky ends from other [i]almost] patterns.

This will carry on untill elimination(s) can be made based on the subset counting method.

the trick is to spot these... You can obviously imagine how complex they might be in a busy PM grid.

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Postby Gerra » Wed May 21, 2008 10:38 am

Thanks for the reply.
As I new to this community, I can hardly understand what you mean Sticky Ends.

But Almosting works, isn't?

...We can imagine two Almost AIC both targeting the same candidate(s) connected with XY-Chain, or two Almost ALS-XY-Wing whose restricted commons are connected with an AIC containing additional ALS nodes. Or An Almost Turbot-Fish connected to an Almost Bug-Lite with intersections in their eliminations. Anything Can happen, isn't?
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Postby tarek » Wed May 21, 2008 11:34 am

Gerra wrote:Thanks for the reply.
As I new to this community, I can hardly understand what you mean Sticky Ends.
This is a phrase I'm using to describe weak inferences stemming from a pattern.

in this regard you could imagine the almost pattern as a piece within a jigsaw puzzle .... it needs a compatible piece to fit next to it .... this by itslef would not do anything unless a completete picture is reached ....

the complete picture is the targeted elimination(s) deduced from connecting these pieces.

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Re: Almosting - Try to generialize how ALS works.

Postby ronk » Wed May 21, 2008 12:44 pm

Gerra wrote:"-If the candidate 4 in r6c6 is false, then the classic Almost Locked Set (orange candidates) in c6 kills the red 6.

After r6c6<>4, r236c6 would still hold {1468} because of candidate 4 in r3c6. IOW your ALS wouldn't become "locked" and r5c6<>6 would not be valid.

-If the candidate 4 in r6c6 is false ...
-If the candidate 4 in r4c5 is false ...
-If the candidate 4 in r4c6 is false ...
-If the candidate 4 in r4c4 is false ...

If you were going the "if .... is true" route, then you would need all four. When going the "if ... is false" route, two are sufficient.
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Re: Almosting - Try to generialize how ALS works.

Postby Gerra » Wed May 21, 2008 1:27 pm

ronk wrote:...candidate 4 in r3c6...

I didn't put candidate 4 into r3c6.
If I'd put, the ALS couldn't has been locked, just as you said.

Anyway, the point of this thread is not the ALS.
The other Almost Patterns are more interesting.
The Almost X-wing, and the Almost X-chain are fully enough to make the red elimination (or any two Almost Patterns, Chains, Sets). One of them must be repaired, so the red 6 must go.
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Re: Almosting - Try to generialize how ALS works.

Postby ronk » Wed May 21, 2008 1:59 pm

Gerra wrote:
ronk wrote:...candidate 4 in r3c6...

I didn't put candidate 4 into r3c6.

Look at your graphic. There is a candidate 4 in r3c6.
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Re: Almosting - Try to generialize how ALS works.

Postby Gerra » Wed May 21, 2008 2:28 pm

ronk wrote:There is a candidate 4 in r3c6.

In the cell can be found in the intersection of the third row, and the sixth column I can only see three orange coloured candidate (1|6|8). Does not matter.

Here comes a deduction I've made with Single Digit ALS.

Image

All starts with a Strong Pair of 6 in row 6.
If the green marked 6 is true, it locks the ALS (9|3) in r89c5, what forces an instance of 9 into r3c6 trough the strong link of 9-s in box 2.
If the blue marked 6 of the conjugate pair is true, it repairs the Almost Pointing Pair, what excludes the candidate 8 in the cell r5c1, what forces an instance of 9 into r5c1 since it is a bivalue (strong linked) cell. The candidate 9 in cell r3c1 sees all the possible 9 instances, so the chain kills it.

The Almost Pointing Pair is marked purple in the Pattern Graph of 8-s below the table.

Of course, this chain can be interpreted as an AIC from 9 in r5c1 to the other 9 in r3c6, with Grouped, and ALS nodes.
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Re: Almosting - Try to generialize how ALS works.

Postby ronk » Wed May 21, 2008 2:49 pm

Gerra wrote:
ronk wrote:There is a candidate 4 in r3c6.

In the cell can be found in the intersection of the third row, and the sixth column I can only see three orange coloured candidate (1|6|8). Does not matter.

I'm reminded of why I've never liked reading someone else's hand-written graphics.

Sorry, your '1' looked like a '4' to me ... still does.
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Re: Almosting - Try to generialize how ALS works.

Postby Gerra » Wed May 21, 2008 3:11 pm

Well, the hand-writtens can be easily misreaded.
I tried to write all of the 1-s to the upper left corner, and so on.
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Postby Gerra » Wed May 21, 2008 10:06 pm

Let me explain what I mean Almost X-Chain trough a real example.

There is a triple of 6 present in box 2 linked weak, so two of them must be false.

Image

-If the candidate 6 in r1c5 (marked purple) is false, the Almost X-Chain become repaired, so the red marked candidate of 6 in r3c1 cannot be true.

-Supposing the candidate 6 in r3c4 (marked cyan) is false on one hand it closes the Almost Locked set in r3c24 (7|9) what eliminates the candidate 9 in r3c6. On the other hand the false 6 in r3c4 forces candidate 2 to be true in r4c6 trough the AIC drawn, what eliminates the candidate 2 in r3c6. After this, in this case the only remaining candidate in r3c6 is 6, what eliminates the red marked candidate 6 in r3c1.

According the initial weak link of 6-s in box 2 one of the two cases above must be true, therefore I can eliminate the red marked 6.
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