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[tarek]

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+-------+-------+-------+
| 8 . . | . . . | . 4 . |
| . . 5 | 4 9 . | . . 7 |
| . . 1 | . . 7 | 2 . . |
+-------+-------+-------+
| 3 . . | 5 . . | 1 . . |
| . 9 . | . . . | . 6 . |
| . . . | . . 4 | . 3 . |
+-------+-------+-------+
| . 8 . | . . . | 5 1 . |
| 2 . 7 | . 4 . | . . . |
| . 1 . | . . 8 | . . 4 |
+-------+-------+-------+
8......4...549...7..1..72..3..5..1...9.....6......4.3..8....51.2.7.4.....1...8..4


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[SpAce]

Code: Select all

.-----------------------.-----------------------.----------------------.
| 8       7       3'9"  | 236     5      c23(6) |   9'-6"   4    1     |
| 6       2       5     | 4       9       1     |   3       8    7     |
| 4"9'    3"4'    1     | 368     368     7     |   2       5    6'9"  |
:-----------------------+-----------------------+----------------------:
| 3      a4"6'    24'68 | 5       2678   b269   |   1       27  a28(9) |
| 17      9       28    | 2378    12378   23    |   4       6    5     |
| 17      5       268   | 26789   12678   4     | d(7)8-9"  3    289   |
:-----------------------+-----------------------+----------------------:
| 4'-9"   8       34"69 | 23679   2367   c2369  |   5       1    236   |
| 2      b3'-6"   7     | 1       4       5     |   68      9    3"68  |
| 5       1      h3(69) | 2369   g236     8     |  e67     f27   4     |
'-----------------------'-----------------------'----------------------'

Medusa coloring: candidates in each parity (' or ") are equivalent, i.e. true or false together.

A derived SIS to prove one parity false:

Code: Select all

7x7 PM
------

 9r4c9 9r4c6
 6r1c6 6r4c6 6r7c6
 7r6c7             7r9c7
                   7r9c8 2r9c8
             6r9c5       2r9c5 3r9c5
 9r9c3                         3r9c3 6r9c3
 6r9c3                         3r9c3 9r9c3     
------------------------------------------

-> (9r4c9|6r1c6|7r6c7|6r9c3|9r9c3) - (9"r6c7 & 6"r1c7 & 9"r7c1 & 6"r8c2) => "-parity is false; stte

In other words, every member of the SIS sees at least one candidate of the "-parity, which means that at least one "-candidate must be false. Since all candidates in a Medusa parity are true or false together, it follows that all candidates in the "-parity can be immediately eliminated, and all candidates of the opposite '-parity placed.

[Cenoman]

Code: Select all

 +-------------------+-------------------------+-------------------+
 |  8    7    39     |  236     5      A236*   |  9-6   4    1     |
 |  6    2    5      |  4       9       1      |  3     8    7     |
 | a49^ a34^  1      |  368     368     7      |  2     5 Dda69^*  |
 +-------------------+-------------------------+-------------------+
 |  3    46   2468   |  5       2678   B269*   |  1     27  C289*  |
 |  17   9    28     |  2378    12378   23     |  4     6    5     |
 |  17   5    268    |  26789   12678   4      |  789   3    289   |
 +-------------------+-------------------------+-------------------+
 |  49   8    3469   |  23679   2367   z2369#  |  5     1   y236#  |
 |  2   b36^  7      |  1       4       5      |  68    9   c368^  |
 |  5    1    369    |  2369    236     8      |  67    27   4     |
 +-------------------+-------------------------+-------------------+

[(6=493)r3c129 - r8c2 = (3-6)r8c9 = (6)r3c9] = r7c9 - r7c6 = [(6)r1c6 = (6-9)r4c6 = r4c9 - (9=6)r3c9] => -6r1c7; ste
...two almost M-wings (^, *), targetting the same PE, with two conflicting spoilers (#) => at least one wing is true.

My first version (the way I found it):

Hidden Text: Show

Double kraken (6)r378c9 & (6)r147c6 (almost M2-wing)
(6)r3c9
(6)r7c9 - r7c6 = [(6)r1c6=(6-9)r4c6=r4c9-(9=6)r3c9]
(6-3)r8c9 = r8c2 - (3=496)r3c129
-------------
=>-6r1c7; ste

... and the 7x7 unfolded TM:

Hidden Text: Show

Code: Select all

6r3c9 9r3c9
      9r3c1 4r3c1
            4r3c2 3r3c2
                  3r8c2 3r8c9
6r3c9                   6r8c9 6r7c9
6r1c6                         6r7c6 6r4c6
      9r4c9                         9r4c6
-------------
=>-6r1c7; ste