Slice of Pi

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Slice of Pi

Postby mith » Mon Sep 21, 2020 8:46 pm

Code: Select all
+-------+-------+-------+
| . . 3 | . . . | 1 . . |
| . . . | 4 . 1 | . 5 . |
| 9 . 2 | . . . | . . . |
+-------+-------+-------+
| . 6 . | . . 5 | . 3 . |
| 5 . 8 | . . . | 9 . 7 |
| . 9 . | 3 . . | . 2 . |
+-------+-------+-------+
| . . . | . . . | 3 . 8 |
| . 4 . | 6 . 2 | . . . |
| . . 6 | . . . | 4 . . |
+-------+-------+-------+
..3...1.....4.1.5.9.2.......6...5.3.5.8...9.7.9.3...2.......3.8.4.6.2.....6...4..
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Re: Slice of Pi

Postby pjb » Mon Sep 21, 2020 10:32 pm

Code: Select all
 4       5       3      |b28     2679   679    | 1     c78     69     
 6       8       7      | 4      39     1      | 2      5      39     
 9       1       2      | 58     3567   367    | 67     478    346   
------------------------+----------------------+---------------------
 2       6       14     | 79     79     5      | 8      3      14     
 5       3       8      |a12     1246   46     | 9      4-1    7     
 7       9       14     | 3      148    48     | 56     2      56     
------------------------+----------------------+---------------------
 1       2       5      | 79     479    479    | 3      6      8     
 38      4       9      | 6      38     2      | 57    d17     15     
 38      7       6      | 15     15     38     | 4      9      2     

(1=2)r5c4 - (2=8)r1c4 - (8=7)r1c8 - (7=1)r8c8 => -1 r5c8; stte

Phil
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Re: Slice of Pi

Postby SpAce » Mon Sep 21, 2020 11:12 pm

Yet another funny solution.

Code: Select all
.-----------.--------------------.------------------.
| 4   5  3  | c28   d679+2  679+ | 1   c78     69+  |
| 6   8  7  |  4     39+    1    | 2    5      39+  |
| 9   1  2  | e58   d367+5  367  | 67  b78-4  a36+4 |
:-----------+--------------------+------------------:
| 2   6  14 |  79+   79+    5    | 8    3      14   |
| 5   3  8  | f12    1246   46   | 9   f14     7    |
| 7   9  14 |  3     148    48   | 56   2      56   |
:-----------+--------------------+------------------:
| 1   2  5  |  79+   479+   479+ | 3    6      8    |
| 38  4  9  |  6     38     2    | 57   17     15   |
| 38  7  6  | e15    15     38   | 4    9      2    |
'-----------'--------------------'------------------'

MUG+3 (34679) b2p2358,b3p369,b5p12,b8p123 (hoping it's correct...)

(4)r3c9 == [(8)r3c8 = (82)r1c84 - (2==5)r13c5 - (51)r39c4 = (14)r5c48] => -4 r3c8; stte

(Even if it's valid, it makes little sense. The 2 and 5 are much more simply strongly-linked due to the ALS (256789)b2p23589. But hey, MUGs are fun. Can someone find a more reasonable uniqueness solution?)

something simpler: Show
Code: Select all
.-----------.----------------.----------------.
| 4   5  3  | b28  2679  679 | 1   b78    69  |
| 6   8  7  |  4   39    1   | 2    5     39  |
| 9   1  2  |  58  3567  367 | 67  c78-4  346 |
:-----------+---- -----------+----------------:
| 2   6  14 |  79  79    5   | 8    3     14  |
| 5   3  8  | a12  1246  46  | 9   a14    7   |
| 7   9  14 |  3   148   48  | 56   2     56  |
:-----------+----- ----------+----------------:
| 1   2  5  |  79  479   479 | 3    6     8   |
| 38  4  9  |  6   38    2   | 57   17    15  |
| 38  7  6  |  15  15    38  | 4    9     2   |
'-----------'----------------'----------------'

(4=12)r5c84 - (28)r1c48 = (8)r3c8 => -4 r3c8; stte
-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: Slice of Pi

Postby Cenoman » Tue Sep 22, 2020 5:25 pm

Code: Select all
 +-----------------+--------------------+-------------------+
 |  4    5    3    | b28 Aa2679*  679*  |  1  zc78    69    |
 |  6    8    7    |  4    39     1     |  2    5     39    |
 |  9    1    2    |  58   3567  x367   | y67 zd78-4  346   |
 +-----------------+--------------------+-------------------+
 |  2    6    14   |  79*  79*    5     |  8    3     14    |
 |  5    3    8    | C12  B1246   46    |  9   C14    7     |
 |  7    9    14   |  3    148    48    |  56   2     56    |
 +-----------------+--------------------+-------------------+
 |  1    2    5    |  79*  479    479*  |  3    6     8     |
 |  38   4    9    |  6    38     2     |  57   17    15    |
 |  38   7    6    |  15   15     38    |  4    9     2     |
 +-----------------+--------------------+-------------------+

BUG-lite (79)r1c56, r4c45, r7c46 using mixed internals-external
(2)r1c5 - (2=8)r1c4 - r1c8 = (8)r3c8
(6-2)r1c5 = r5c5 - (2=14)r5c48
(7)r3c6 - r3c7 = (78)r13c8
=> -4 r3c8; ste
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Re: Slice of Pi

Postby SpAce » Wed Sep 23, 2020 12:03 am

Cenoman wrote:BUG-lite (79)r1c56, r4c45, r7c46 using mixed internals-external

Thanks, you did it! I started with that pattern but failed to find anything I liked, so I ended up bloating it into the horrible MUG. I thought I considered that set of guardians too but maybe I didn't. Or perhaps I just didn't see a short solution with them, can't remember.

Unfortunately your solution seems to have a similar problem to mine. As far as I see, it's also degenerate because it contains a simpler strong link (2r1c5 is used both on and off). Perhaps there simply isn't any uniqueness solution here that would actually make sense, but who cares. They're still fun!
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