March 4, 2017

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March 4, 2017

Postby ArkieTech » Sat Mar 04, 2017 12:40 am

Code: Select all
 *-----------*
 |..9|...|.58|
 |...|.7.|..9|
 |...|..5|..1|
 |---+---+---|
 |..3|96.|1..|
 |.4.|...|.9.|
 |..7|.14|2..|
 |---+---+---|
 |4..|8.1|...|
 |9..|.2.|...|
 |781|...|3..|
 *-----------*


Play/Print this puzzle online
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Re: March 4, 2017

Postby Leren » Sat Mar 04, 2017 12:48 am

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     2-7    | 1     478  a47     |
| 1     4     26     | 237   8     237    | 5     9     67     |
| 68    9     7      | 5     1     4      | 2     68    3      |
|--------------------+--------------------+--------------------|
| 4     26    256    | 8     3     1      | 9     67    567    |
| 9     3     56     |c467   2    d67     | 8     1    b456    |
| 7     8     1      | 46    5     9      | 3     46    2      |
*--------------------------------------------------------------*

M Wing Type 2A : (7=4) r4c9 - r8c9 = (4-7) r8c4 = (7) r8c6 => - 7 r4c6; stte

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Re: March 4, 2017

Postby SteveG48 » Sat Mar 04, 2017 12:49 am

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     2-7   | 1    b478  a47    |
 | 1     4     26    | 237   8     237   | 5     9     67    |
 | 68    9     7     | 5     1     4     | 2     68    3     |
 *-------------------+-------------------+-------------------|
 | 4     26    256   | 8     3     1     | 9     67    567   |
 | 9     3     56    | 467   2    d67    | 8     1     456   |
 | 7     8     1     |d46    5     9     | 3    c46    2     |
 *-----------------------------------------------------------*


(7=4)r4c9 - r4c8 = r9c8 - (4=67)b8p67 => -7 r4c6 ; stte
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Re: March 4, 2017

Postby Marty R. » Sat Mar 04, 2017 1:18 am

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  | 1 478 47  |
| 1   4   26  | 237  8 237 | 5 9   67  |
| 68  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   |
+-------------+------------+-----------+

Play this puzzle online at the Daily Sudoku site

W-Wing (67)b68, SL7c4 w' transport

(6=7)r5c9-r5c4=r8c4-(7=6)r8c6-r9c4=r9c8=> -6r6c8,r78c9
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Re: March 4, 2017

Postby Alex_Popov_92 » Sat Mar 04, 2017 6:37 am

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     2-7   | 1     478  b47    |
 | 1     4     26    | 237   8     237   | 5     9     67    |
 | 68    9     7     | 5     1     4     | 2     68    3     |
 *-------------------+-------------------+-------------------|
 | 4     26    256   | 8     3     1     | 9     67    567   |
 | 9     3     a56   | 467   2    a67    | 8     1     a456  |
 | 7     8     1     | 46    5     9     | 3    46     2     |
 *-----------------------------------------------------------*

ALS xz-rule
ALS a r8c369, ALS b r4c9,x=4, z=7
=> r4c6<>7
(7=4)r8c369 - (4=7)r4c9 => r4c6<>7; stte
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Re: March 4, 2017

Postby Alex_Popov_92 » Sat Mar 04, 2017 7:05 am

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     c27   | 1     478   d47   |
 | 1     4     26    | 237   8     237   | 5     9     67    |
 | 68    9     7     | 5     1     4     | 2     68    3     |
 *-------------------+-------------------+-------------------|
 | 4     26    256   | 8     3     1     | 9     67    567   |
 | 9     3      56   | a467   2    b67   | 8     1     e456  |
 | 7     8     1     | 46    5     9     | 3    46     2     |
 *-----------------------------------------------------------*

(4-7)r8c4 = 7r8c6 - r4c6 = (7-4)r4c9 = 4r8c9;
=> r8c4<>4 stte
Last edited by Alex_Popov_92 on Sat Mar 04, 2017 10:28 pm, edited 1 time in total.
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Re: March 4, 2017

Postby Ngisa » Sat Mar 04, 2017 10:16 am

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 2-7  | 1 478 a47  |
| 1   4   26  | d237  8 237 | 5 9   6-7  |
| 68  9   7   | 5    1 4   | 2 68  3   |
+-------------+------------+-----------+
| 4   26  256 | 8    3 1   | 9 67  567 |
| 9   3   56  | c467  2 67  | 8 1   b456 |
| 7   8   1   | 46   5 9   | 3 46  2   |
+-------------+------------+-----------+

(7=4)r4c9 - r8c9 = (4-7)r8c4 = (7)r5c4 => - 7 r5c9, r4c6; stte

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Re: March 4, 2017

Postby bat999 » Sat Mar 04, 2017 3:34 pm

This is a solution I came up with (same result as Marty R above).
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    |
:-----------------+----------------+----------------:
| b258  b25   3   |  9     6  b27  | 1  c478  c47   |
|  1     4    26  |  237   8   237 | 5   9    c67   |
|  68    9    7   |  5     1   4   | 2   8-6   3    |
:-----------------+----------------+----------------:
|  4     26   256 |  8     3   1   | 9   67    57-6 |
|  9     3    56  |  467   2  b67  | 8   1     45-6 |
|  7     8    1   | b46    5   9   | 3  a46    2    |
'-----------------'----------------'----------------'
(6=4)r9c8 - (4=8)r4c126,r8c6,r9c4 - (8=6)4c89,r5c9 => -6 r6c8,r78c9; stte

See that middle node (4=8)r4c126,r8c6,r9c4?
It says to me "NOT4 in r4c126,r8c6,r9c4 forces 8 in r4c126,r8c6,r9c4".
Or "If 4 is false then 8 is true in r4c126,r8c6,r9c4".

It's behaving like an ALS. :o

Usually when I use an ALS I consider cells in the same house.
When we remove candidate(s) the position of the remaining candidates gives us a useful result.
The cells are restricted because we're only allowed one of a candidate in a house - that's the restriction that locks the set.

In my middle node above the cells are not in the same house.
But they are restricted because when we remove the 4 it forces the remaining candidates into a position that gives us a useful result.
It's a different flavour of restriction - but it's still a restriction that locks the set.

Is there a particular name for this type of ALS?

I'm starting to think about the Sudoku grid as a set of 81 cells.
And any selection from those cells is a subset no matter where they are.
And if removing candidate(s) from the subset gives us a useful result then I will treat it as I would a conventional ALS. ;)
8-)
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Re: March 4, 2017

Postby Sudtyro2 » Sat Mar 04, 2017 3:50 pm

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     |
 |--------------------+-------------------+-------------------|
 | b258  b25    3     | 9     6    c27    | 1     478  c47    |
 |  1     4    a26    | 237   8     237   | 5     9     67    |
 |  68    9     7     | 5     1     4     | 2     68    3     |
 |--------------------+-------------------+-------------------|
 |  4     26   f56-2  | 8     3     1     | 9     67    567   |
 |  9     3    e56    | 467   2    c67    | 8     1    d456   |
 |  7     8     1     | 46    5     9     | 3     46    2     |
 *------------------------------------------------------------*
Myth's CoALS Rule applied to the two overlapping ALS marked 'c'.

2r5c3 = r4c12 - (27=46)r4c69,r8c6 - (4|6=5)r8c9 - r8c3 = 5r7c3 => -2r7c3; stte

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Re: March 4, 2017

Postby Sudtyro2 » Sat Mar 04, 2017 4:17 pm

bat999 wrote: ...
See that middle node (4=8)r4c126,r8c6,r9c4?
It says to me "NOT4 in r4c126,r8c6,r9c4 forces 8 in r4c126,r8c6,r9c4".

Hi Bat,
Isn't your middle node just the equivalent of two linking ALS?
(4=67)r9c4,r8c6 - (7=258)r4c126 => 4r9c4=8r4c1

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Re: March 4, 2017

Postby bat999 » Sat Mar 04, 2017 6:12 pm

Sudtyro2 wrote:... the equivalent of two linking ALS?
Yes
The two linking ALS...
(4=67)r9c4,r8c6 - (7=258)r4c126
which is same as...
(4=7)r9c4,r8c6 - (7=8)r4c126

And my solution would be...
(6=4)r9c8 - (4=7)r9c4,r8c6 - (7=8)r4c126 - (8=6)4c89,r5c9 => -6 r6c8,r78c9; stte
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"?
8-)
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Re: March 4, 2017

Postby Cenoman » Sat Mar 04, 2017 8:51 pm

Code: Select all
 +-------------------+-------------------+------------------+
 |b236  a126   9     | 1236   4    23-6  | 7    5     8     |
 | 235   125   4     | 123    7    8     | 6    23    9     |
 |b236   7     8     | 236    9    5     | 4    23    1     |
 +-------------------+-------------------+------------------+
 |d258  d25    3     | 9      6   d27    | 1    478   47    |
 | 1     4     26    | 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     56    | 467    2   e67    | 8    1     456   |
 | 7     8     1     | 46     5    9     | 3    46    2     |
 +-------------------+-------------------+------------------+

(6)r1c2 = r13c1 - (6=8)r6c1 - (8=7)r4c126 - (7=6)r8c6 => -6 r1c6; stte

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Re: March 4, 2017

Postby Sudtyro2 » Sat Mar 04, 2017 8:58 pm

bat999 wrote: 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"?

My understanding (usually limited) is that an ALS, AALS, AAALS, etc. has all of its digits contained within the same house. Otherwise, you have the more general structure called a Subset.
E.g., in my earlier CoALS Rule posting, the fourth node is an AALS, but the third node, having four digits in three cells, is not an ALS, but rather a special subset formed by overlapping two true ALS, and it uses special linking rules. Maybe the experts can help us out further!

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Re: March 4, 2017

Postby JasonLion » Sat Mar 04, 2017 10:26 pm

From my point of view this is simply two ALS, both of which are used as links in an AIC. Some might call it an ALS-XZ.
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Re: March 4, 2017

Postby bat999 » Sat Mar 04, 2017 10:33 pm

Sudtyro2 wrote:... an ALS, AALS, AAALS, etc. has all of its digits contained within the same house. Otherwise, you have the more general structure called a Subset.

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".
Or "If 5 is false then 2 is true in r48c69".
8-)
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