July 16, 2020

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July 16, 2020

Postby tarek » Thu Jul 16, 2020 8:48 am

Code: Select all
+-------+-------+-------+
| . . . | 6 8 3 | . . . |
| . 9 . | . . . | . 8 . |
| . . . | 5 . . | 3 . . |
+-------+-------+-------+
| . 1 . | . . . | . . 3 |
| . . 2 | . . . | . . 6 |
| 3 . 5 | 2 . . | 9 . 4 |
+-------+-------+-------+
| 2 8 . | 4 7 . | . . . |
| . . 7 | . . 6 | . 5 . |
| . . 1 | 3 . . | . . . |
+-------+-------+-------+
...683....9.....8....5..3...1......3..2.....63.52..9.428.47......7..6.5...13.....

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Re: July 16, 2020

Postby yzfwsf » Thu Jul 16, 2020 9:07 am

Code: Select all
.-------------.-------------.--------------.
| 157  a25 4  | 6  8    3   | 1-2 9   1257 |
| 567  9   3  | 1  24   27  | 46  8   257  |
| 167  26  8  | 5  249  279 | 3   46  127  |
:-------------+-------------+--------------:
| 69   1   69 | 7  5    4   | 8   2   3    |
| 8    4   2  | 9  3    1   | 5   7   6    |
| 3    7   5  | 2  6    8   | 9   1   4    |
:-------------+-------------+--------------:
| 2    8   69 | 4  7    5   | 16  3   19   |
| 49   3   7  | 8  1    6   | d24 5   29   |
| 456  b56 1  | 3  29   29  | 7   c46 8    |
'-------------'-------------'--------------'

(2=5)r1c2-(5=6)r9c2-(6=4)r9c8-(4=2)r8c7 => -2r1c7;stte
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Re: July 16, 2020

Postby Cenoman » Thu Jul 16, 2020 9:42 am

Code: Select all
 +------------------+-------------------+-------------------+
 |  157   25   4    |  6    8     3     | d12   9    1257   |
 |  567   9    3    |  1    24    27    |  46   8    257    |
 |  167  b26   8    |  5    249*  279*  |  3    46  c127    |
 +------------------+-------------------+-------------------+
 |  69    1    69   |  7    5     4     |  8    2    3      |
 |  8     4    2    |  9    3     1     |  5    7    6      |
 |  3     7    5    |  2    6     8     |  9    1    4      |
 +------------------+-------------------+-------------------+
 |  2     8    9-6  |  4    7     5     | d16   3    19     |
 |  49    3    7    |  8    1     6     |  24   5    29     |
 |  456  a56   1    |  3    29*   29*   |  7    46   8      |
 +------------------+-------------------+-------------------+

UR(29)r39c56 using externals
(6)r9c2 = (6-2)r3c2 == r3c9 - (2=16)r17c7 => -6 r7c3; ste
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Re: July 16, 2020

Postby Ngisa » Thu Jul 16, 2020 1:19 pm

Code: Select all
+--------------------+-------------------+---------------------+
| 157     5-2     4  | 6     8       3   | a12     9      1257 |
|c567     9       3  | 1     24      27  |b46      8      257  |
| 167    d26      8  | 5     249     279 | 3       46     127  |
+--------------------+-------------------+---------------------+
| 69      1       69 | 7     5       4   | 8       2      3    |
| 8       4       2  | 9     3       1   | 5       7      6    |
| 3       7       5  | 2     6       8   | 9       1      4    |
+--------------------+-------------------+---------------------+
| 2       8       69 | 4     7       5   |a16      3      19   |
| 49      3       7  | 8     1       6   | 24      5      29   |
| 456     56      1  | 3     29      29  | 7       46     8    |
+--------------------+-------------------+---------------------+

(2=16)r17c7 - (6)r2c7 = r2c1 - (6=2)r3c2 => - 2r1c2; stte

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Re: July 16, 2020

Postby SpAce » Thu Jul 16, 2020 2:57 pm

Code: Select all
.-----------------.-------------.------------------.
|  157+   25  4   | 6  8    3   |  12  9     157+2 |
|  57+6   9   3   | 1  24   27  |  46  8     57+2  |
|  17+6   26  8   | 5  249  279 |  3   46    17+2  |
:-----------------+-------------+------------------:
|  69     1   69  | 7  5    4   |  8   2     3     |
|  8      4   2   | 9  3    1   |  5   7     6     |
|  3      7   5   | 2  6    8   |  9   1     4     |
:-----------------+-------------+------------------:
|  2      8   9-6 | 4  7    5   | b16  3    b9#1   |
|  49     3   7   | 8  1    6   |  24  5     29    |
| a46#5  a56  1   | 3  29   29  |  7   4-6   8     |
'-----------------'-------------'------------------'

MUG(157)r123c19+5 using #externals

(65)r9c21 == (16)r7c97 => -6 r7c3,r9c8
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."
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Re: July 16, 2020

Postby Cenoman » Thu Jul 16, 2020 3:35 pm

SpAce wrote:MUG(157)r123c19+5 using #externals
(65)r9c21 == (16)r7c97 => -6 r7c3,r9c8

Nice !
I'd seen it a little time after posting my solution. I was expecting someone found it. You did !
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Re: July 16, 2020

Postby rjamil » Thu Jul 16, 2020 3:56 pm

yzfwsf wrote:(2=5)r1c2-(5=6)r9c2-(6=4)r9c8-(4=2)r8c7 => -2r1c7;stte

::: OR :::

Code: Select all
 +----------------+-------------+-----------------+
 | 157  (25)  4   | 6  8    3   | (12)  9    1257 |
 | 567  9     3   | 1  24   27  | 46    8    257  |
 | 167  26    8   | 5  249  279 | 3     46   127  |
 +----------------+-------------+-----------------+
 | 69   1     69  | 7  5    4   | 8     2    3    |
 | 8    4     2   | 9  3    1   | 5     7    6    |
 | 3    7     5   | 2  6    8   | 9     1    4    |
 +----------------+-------------+-----------------+
 | 2    8     9-6 | 4  7    5   | (16)  3    19   |
 | 49   3     7   | 8  1    6   | 24    5    29   |
 | 456  (56)  1   | 3  29   29  | 7     4-6  8    |
 +----------------+-------------+-----------------+

ALS move: 1256 @ r19c2 r17c7 => -6 @ r7c3 r9c8; stte

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Re: July 16, 2020

Postby SpAce » Thu Jul 16, 2020 4:36 pm

Cenoman wrote:Nice !
I'd seen it a little time after posting my solution. I was expecting someone found it. You did !

Thanks, Cenoman! You shouldn't expect me to find any MUGs, though, because spotting them is an extremely rare feat for me :) I envy your and eleven's skills in that department. In fact, my confidence with them is so shaky that I had to double-check even this simple one with blue's program to trust that it was a valid MUG. (In this case it's pretty easy to check manually, too, of course.)
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Re: July 16, 2020

Postby SteveG48 » Thu Jul 16, 2020 4:42 pm

Code: Select all
 *-----------------------------------------------------------*
 | 157  b25    4     | 6     8     3     | 1-2   9     1257  |
 | 567   9     3     | 1     24    27    | 46    8     257   |
 | 167   26    8     | 5     249   279   | 3     46    127   |
 *-------------------+-------------------+-------------------|
 | 69    1     69    | 7     5     4     | 8     2     3     |
 | 8     4     2     | 9     3     1     | 5     7     6     |
 | 3     7     5     | 2     6     8     | 9     1     4     |
 *-------------------+-------------------+-------------------|
 | 2     8     69    | 4     7     5     | 16    3     19    |
 | 49    3     7     | 8     1     6     |a24    5     29    |
 | 456  b56    1     | 3     29    29    | 7    a46    8     |
 *-----------------------------------------------------------*


(2=46)b9p48 - (6=52)r19c2 => -2 r1c7 ; stte

Uh-oh. Looks like I came up with the same as yzfwsf, except backwards.

Or, (6=52)r19c2 - (2=16)r17c7 => -6 r7c3,r9c8 , but it's still not much different.
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Re: July 16, 2020

Postby Sudtyro2 » Fri Jul 17, 2020 11:35 am

Code: Select all
+----------------+-------------+-----------------+
| 157  25*   4   | 6  8    3   | 12*   9    1257 |
| 567  9     3   | 1  24   27  | 46    8    257  |
| 167  26    8   | 5  249  279 | 3     46   127  |
+----------------+-------------+-----------------+
| 69   1     69  | 7  5    4   | 8     2    3    |
| 8    4     2   | 9  3    1   | 5     7    6    |
| 3    7     5   | 2  6    8   | 9     1    4    |
+----------------+-------------+-----------------+
| 2    8     9-6 | 4  7    5   | 16*   3    19   |
| 49   3     7   | 8  1    6   | 24    5    29   |
| 456  56*   1   | 3  29   29  | 7     4-6  8    |
+----------------+-------------+-----------------+

Another example of an easy chainless solution via Subset Counting...

The four marked cells (1256)c2r19,c7r17, courtesy of rjamil, form a locked subset. However, only the 6-digit can occur twice in the subset. So, any true external 6-digit that can see both 6s in the subset would leave four cells to house three digits, an impossibility. Hence, 6r7c3 and 6r9c8 must both be false.

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Re: July 16, 2020

Postby tarek » Fri Jul 17, 2020 11:59 am

Sudtyro2 wrote:Another example of an easy chainless solution via Subset Counting...
I thought that you can prove most if not all (sticky end) eliminations using subset counting ... It is a powerful technique but does involve search & analysis limiting its practicality. The capabilities are even enhanced when displacements are introduced using chains, but even then, you can include the entire chain in your bigger subset as long as you still like counting at that stage!

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