March 4, 2017

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Re: March 4, 2017

Postby JC Van Hay » Sat Mar 04, 2017 11:26 pm

bat999 wrote: But now it has four nodes instead of three. :roll:

Are you suggesting that there isn't a particular name for this type of ALS with cells not all in the same house?
That it is just the compression of two linking ALS and that it is still known only as "ALS"?
Nothing prevents the use of derived strong links in a "proof" :
ALS(2578)r4c126 -> 7r4c6==8r4c1
ALS(467)r8c6.r9c -> 7r8c6==4r9c4
Therefore, as suggested by JasonLion, "flightless" ALS-XZ Rule : 4r9c4==7r8c6-7r4c6==8r4c1 -> 4r9c4===8r4c1
ALS(4678)r4c89.r8c9 -> 8r4c8==6r5c9
where a multiple = indicates the "level" of a derived strong link.

This allows to write (6=4)r9c8-4r9c4===8r4c1-8r4c8==6r5c9 -> -6r6c8.r78c9

What is ~embarassing, however, is the use of all the cells in R4 [a continuous network].

If you want to "reduce" the number of "nodes", than don't use all the cells in R4!
For example : using ALS(468)r6c89 -> 8r6c8==4r9c8,
Code: Select all
+------------------+---------------+--------------+
| 236    126   9   | 1236  4  236  | 7  5     8   |
| 235    125   4   | 123   7  8    | 6  23    9   |
| 236    7     8   | 236   9  5    | 4  23    1   |
+------------------+---------------+--------------+
| (258)  (25)  3   | 9     6  (27) | 1  47-8  47  |
| 1      4     26  | 237   8  237  | 5  9     67  |
| 6-8    9     7   | 5     1  4    | 2  (68)  3   |
+------------------+---------------+--------------+
| 4      26    256 | 8     3  1    | 9  67    567 |
| 9      3     56  | 467   2  (67) | 8  1     456 |
| 7      8     1   | (46)  5  9    | 3  (46)  2   |
+------------------+---------------+--------------+
ALS-XY Wing[8r6c8==4r9c8-4r9c4==7r8c6-7r4c6==8r4c1] or 8r6c8==4r9c8-4r9c4===8r4c1 or ... -> -8r4c8.r6c1; stte
bat999 wrote:Code: Select all
Code: Select all
.-------------------.---------------.--------------.
|  236   126   9    | 1236  4   236 | 7  5     8   |
|  235   125   4    | 123   7   8   | 6  23    9   |
|  236   7     8    | 236   9   5   | 4  23    1   |
:-------------------+---------------+--------------:
| c258  c25    3    | 9     6  b27  | 1  478  b47  |
|  1     4     2-6  | 237   8   237 | 5  9     67  |
| c68    9     7    | 5     1   4   | 2  68    3   |
:-------------------+---------------+--------------:
|  4     26    256  | 8     3   1   | 9  67    567 |
|  9     3    a56   | 467   2  b67  | 8  1    b456 |
|  7     8     1    | 46    5   9   | 3  46    2   |
'-------------------'---------------'--------------'


(6=5)r8c3 - (5=2)r48c69 - (2=6)r4c12,r6c1 => -6 r5c3; stte

OK, maybe we can use a term "Almost Locked Subset" as in the middle node here.
The four cells r4c6,r4c9,r8c6,r8c9 are a subset and have five candidates 2,4,5,6,7.
This (5=2)r48c69 says to me "NOT5 in r48c69 forces 2 in r48c69".
:!: The term "Almost Locked Subset" would be very confusing with the usual abbreviated ALS :!: Furthermore :
1. Here, r48c69 is an Almost XYWing : 5r8c9=*XYWing[(7=6)r8c6-(6=*4)r8c9-(4=7)r4c9]-(7=2)r4c6 or 5r8c9=[7r8c6==7r4c9]-(7=2)r4c6 or 5r8c9==2r4c6
2. If r4c9=24, then r48c69 would be an Almost Continuous Chain : 5r8c9=*Loop[(7=6)r8c6-(6=*4)r8c9-(4=2)r4c9-(2=7)r4c6]-...
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Re: March 4, 2017

Postby bat999 » Sun Mar 05, 2017 9:38 am

JC Van Hay wrote:... This allows to write...
Nah
Both of my solutions are expressed as generic AICs using Eureka notation.

(6=4)r9c8 - (4=8)r4c126,r8c6,r9c4 - (8=6)4c89,r5c9
(6=5)r8c3 - (5=2)r48c69 - (2=6)r4c12,r6c1

The symbols "==" and "===" are not part of my vocabulary.

My question was whether there is a particular name to describe the phenomenon of the middle node.

It could be described as a "ALS whose cells are not all in the same house".
It could be described as a "Subset that is almost locked".
Maybe it doesn't have a name.
8-)
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Re: March 4, 2017

Postby JC Van Hay » Sun Mar 05, 2017 12:16 pm

bat999 wrote:Both of my solutions are expressed as generic AICs using Eureka notation.
(6=4)r9c8 - (4=8)r4c126,r8c6,r9c4 - (8=6)4c89,r5c9
(6=5)r8c3 - (5=2)r48c69 - (2=6)r4c12,r6c1.
:?:
My question was whether there is a particular name to describe the phenomenon of the middle node.

It could be described as a "ALS whose cells are not all in the same house".
It could be described as a "Subset that is almost locked".
Maybe it doesn't have a name.
There is no need to find a name for a condensed form of (or a derived strong link from) an ALS-XY-Chain. Just imagine how strange it would be to write an ALS-XY-Wing step as a single node :?: Furthermore, "Almost Locked Set"(ALS) and "Almost Multi-Sector Locked Set"(AMSLS) already have a well defined meaning !
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Re: March 4, 2017

Postby bat999 » Sun Mar 05, 2017 1:00 pm

JC Van Hay wrote:... "Almost Multi-Sector Locked Set"(AMSLS)...

Are you suggesting that the answer to my question is "Almost Multi-Sector Locked Set"?
Or are you suggesting that there isn't a particular name for those middle nodes in my solutions?
8-)
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Re: March 4, 2017

Postby JC Van Hay » Sun Mar 05, 2017 1:13 pm

bat999 wrote:
JC Van Hay wrote:... "Almost Multi-Sector Locked Set"(AMSLS)...

Are you suggesting that the answer to my question is "Almost Multi-Sector Locked Set"?
No, because an MSLS is a continuous network.
Or are you suggesting that there isn't a particular name for those middle nodes in my solutions?
Yes, no need for it.
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Re: March 4, 2017

Postby bat999 » Sun Mar 05, 2017 3:03 pm

JC Van Hay wrote:
... are you suggesting that there isn't a particular name for those middle nodes in my solutions?
Yes...
OK
:)
8-)
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