May 31,2020

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May 31,2020

Postby yzfwsf » Sun May 31, 2020 11:12 pm

Code: Select all
 *-----------*
 |..9|3.1|...|
 |...|.59|.6.|
 |.6.|.8.|..3|
 |---+---+---|
 |5..|7..|..1|
 |.4.|...|.7.|
 |1..|..2|..9|
 |---+---+---|
 |3..|.7.|.9.|
 |.7.|91.|...|
 |...|8.6|3..|
 *-----------*
..93.1.......59.6..6..8...35..7....1.4.....7.1....2..93...7..9..7.91.......8.63..
yzfwsf
 
Posts: 845
Joined: 16 April 2019

Re: May 31,2020

Postby eleven » Mon Jun 01, 2020 12:20 pm

Code: Select all
 *-------------------------------------------------------------------*
 |  2478  d258    9       |  3    6     1  |  24578   2458   2458    |
 |  2478   1238   12348   |  24   5     9  | g12478   6      248     |
 |  24     6     e15      |  24   8     7  |  9      f15     3       |
 |------------------------+----------------+-------------------------|
 |  5     d239    236     |  7   c349   8  |  246    b234    1       |
 |  2689   4      2368    |  1    39    5  |  268     7      268     |
 |  1    da38     7       |  6   b34    2  |  458    b3458   9       |
 |------------------------+----------------+-------------------------|
 |  3     d128    1268    |  5    7     4  |  268-1   9      268     |
 |  2468   7      24568   |  9    1     3  |  24568   2458   24568   |
 |  49     159    145     |  8    2     6  |  3       145    7       |
 *-------------------------------------------------------------------*

(3r6c2 -> -3r6c58 -> 34r4c8,r6c5 -> 9r4c5) => -39r1467c2 => 1r7c2 | (5r1c2 -> 1r3c3 -> -1r3c8 -> 1r2c7) => -1r7c7, stte

[Added:] Explanation for the link (1=5)r1467c2:
Since 39 cannot be both there, you have an ALS (1=[39]285)r1467c2, where [39] counts as one digit.
eleven
 
Posts: 3082
Joined: 10 February 2008

Re: May 31,2020

Postby SpAce » Mon Jun 01, 2020 8:10 pm

Code: Select all
.--------------------------.------------.-----------------------.
|   2478  a2[5]8    9      | 3   6    1 | 24578   2458    2458  |
|   2478  i1238   ij12348  | 24  5    9 | 12478   6       248   |
|   24     6      bj15     | 24  8    7 | 9      c15      3     |
:--------------------------+------------+-----------------------:
|   5      239      236    | 7   349  8 | 246     234     1     |
|  g2689   4       h2368   | 1  g39   5 | 268     7       268   |
|   1      38       7      | 6   34   2 | 458     3458    9     |
:--------------------------+------------+-----------------------:
|   3      128      1268   | 5   7    4 | 1268    9       268   |
|   2468   7        24568  | 9   1    3 | 24568   2458    24568 |
| ef9#4    19-5   ek1(5)#4 | 8   2    6 | 3      d1[5]#4  7     |
'--------------------------'------------'-----------------------'

At most one of 4r9c138 can be true, hence (using the implied Almost Turbot Crane):

[(5)r1c2 = r3c3 - r3c8 = (5)r9c8] = 4r9c8 - 4r9c13 = [(9)r9c1 - (93)r5c15 = r5c3 - (3,1)r2c32 = (1,5)r23,9c3] => -5 r9c2; stte

most explicit: Show
[(5)r1c2 = r3c3 - (5=1)r3c8 - (1=5)r9c8] = (4)r9c8 - (4)r9c13 = [(!=9)r9c1 - r5c1 = (9-3)r5c5 = r5c3 - r2c3 = (3-1)r2c2 = r23c3 - (1=5)r9c3] => -5 r9c2; stte

...or cleaner without the contradiction:

[(5)r1c2 = r3c3 - (5=1)r3c8 - (1=5)r9c8] = (4)r9c8 - (4)r9c3 = [(9)r9c2 = r9c1 - r5c1 = (9-3)r5c5 = r5c3 - r2c3 = (3-1)r2c2 = r23c3 - (1=5)r9c3] => -5 r9c2; stte

...or even better with the second part reversed:

[(5)r1c2 = r3c3 - (5=1)r3c8 - (1=5)r9c8] = (4)r9c8 - (4)r9c3 = [(5=1)r9c3 - r23c3 = (1-3)r2c2 = r2c3 - r5c3 = (3-9)r5c5 = r5c1 - r9c1 = (9)r9c2] => -5 r9c2; stte

most compressed: Show
5C8B1\r39c2 = 4r9c8-13 = [9r9c1 - 93r5c15 = r5c3 - 3,1r2c32 = 1,5r23,9c3] => -5r9c2;stte

...or why the hell not:

5C8B1\r39c2=4r9c8-13=[9r9c1-93r5c15=r5c3-3,1r2c32=1,5r23,9c3]=>-5r9c2;stte

(No, I would never write the second variant. Despite my quest for extreme compactness, I don't sacrifice reasonable white space unless absolutely necessary (or if it actually improves readability by highlighting more important parts). It's the second worst offense against readability. The worst is too much white space.)

9x9 TM, or 10x10 BTM unfolded: Show
Code: Select all
 5r1c2 5r3c3
       5r3c8 1r3c8
 5r9c8       1r9c8 4r9c8
                   4r9c1 9r9c1
                         9r5c1 9r5c5
                               3r5c5 3r5c3
                                     3r2c3 3r2c2
                                           1r2c2 1r23c3
 5r9c3             4r9c3                         1r9c3
-------------------------------------------------------
-5r9c2
Code: Select all
 5r1c2 5r3c3
       5r3c8 1r3c8
 5r9c8       1r9c8 4r9c8
                   4r9c1 9r9c1
                         9r5c1 9r5c5
                               3r5c5 3r5c3
                                     3r2c3 3r2c2
                                           1r2c2 1r3c3 1r2c3
                                           1r2c2 1r2c3 1r3c3
 5r9c3             4r9c3                               1r9c3
------------------------------------------------------------
-5r9c2

Or a bit shorter:

Code: Select all
.------------------------.------------.----------------------.
|  2478  d2(5)8    9     | 3   6    1 | 24578   2458   2458  |
|  2478  c1238   bd12348 | 24  5    9 | 12478   6      248   |
|  24     6      bc15    | 24  8    7 | 9      b15     3     |
:------------------------+------------+----------------------:
|  5      239      236   | 7   349  8 | 246     234    1     |
| f2689   4       e2368  | 1  e39   5 | 268     7      268   |
|  1      38       7     | 6   34   2 | 458     3458   9     |
:------------------------+------------+----------------------:
|  3      128      1268  | 5   7    4 | 1268    9      268   |
|  2468   7        24568 | 9   1    3 | 24568   2458   24568 |
| g49    h1(9)-5  a1[45] | 8   2    6 | 3      a1[45]  7     |
'------------------------'------------'----------------------'

(54=1)r9c38 - r23c3&r3c8 = (1-35)b1p59 = (5@|3)b1p26 - (39)r5c35 = r5c1 - r9c1 = (9)r9c2 => -5 r9c2; stte

8x8 TM, or 10x10 BTM unfolded: Show
Code: Select all
 9r9c2   9r9c1
         9r5c1 9r5c5
               3r5c5 3r5c3
                     3r2c3 3r2c2
                           1r2c2 1r23c3
 54r9c38                         1r9c3  1r9c8
                                        1r3c8 1r3c3
 5r1c2                                        5r3c3
---------------------------------------------------
-5r9c2

Code: Select all
 9r9c2 9r9c1
       9r5c1 9r5c5
             3r5c5 3r5c3
                   3r2c3 3r2c2
                         1r2c2 1r2c3 1r3c3
                         1r2c2 1r3c3 1r2c3
 5r9c3                               1r9c3 4r9c3
 5r9c8                                     4r9c8 1r9c8
                                                 1r3c8 1r3c3
 5r1c2                                                 5r3c3
------------------------------------------------------------
-5r9c2
-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."
User avatar
SpAce
 
Posts: 2671
Joined: 22 May 2017

Re: May 31,2020

Postby SpAce » Mon Jun 01, 2020 11:39 pm

eleven wrote:(3r6c2 -> -3r6c58 -> 34r4c8,r6c5 -> 9r4c5) => -39r1467c2 => 1r7c2 | (5r1c2 -> 1r3c3 -> -1r3c8 -> 1r2c7) => -1r7c7, stte

[Added:] Explanation for the link (1=5)r1467c2:
Since 39 cannot be both there, you have an ALS (1=[39]285)r1467c2, where [39] counts as one digit.

Sorry, I couldn't resist...

(1)r2c7 = r3c8 - (1=5)r3c3 - (5)r1c2 = [(1=2389)r7164c2 - r4c5 = (9-3)r5c5 = r5c3 - (3289=1)r1467c2] => -1 r7c7; stte

...or simply:

(1)r2c7 = r3c8 - (1=5)r3c3 - (5)r1c2 = [[(3-9)r5c5] -> (3|9)r5c31 - (3928=1)r4617c2] => -1 r7c7; stte

5x5 TM -> 3x3 PM: Show
Code: Select all
 1r2c7 1r3c8
       1r3c3 5r3c3
 1r7c2       5r1c2 3928r1467c2
                   3r5c3       3r5c5
                   9r5c1       9r5c5
------------------------------------
-1r7c7

Also reveals that (2389)r1467c2 is impossible. Thus:

Code: Select all
 1r2c7 1r3c8
       1r3c3 5r3c3
 1r7c2       5r1c2
------------------
-1r7c7

Not so simple as an unfolded matrix:

14x14 BTM: Show
Code: Select all
 1r2c7 1r3c8
       1r3c3 5r3c3
             5r1c2 2r1c2 8r1c2
                         8r6c2 3r6c2
                               3r5c3 3r5c5
                                     9r5c5 9r5c1
                               3r4c2 ..... 9r4c2 2r4c2
 1r7c2 ................. 8r7c2 ................. 2r7c2
                   2r4c2 ............................. 3r4c2 9r4c2
                                                             9r5c1 9r5c5
                                                                   3r5c5 3r5c3
                                                                         3r6c2 8r6c2
                                                       3r6c2 ................. 8r6c2
 1r7c2 ........... 2r7c2 ..................................................... 8r7c2
------------------------------------------------------------------------------------
-1r7c7
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SpAce
 
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