June 24, 2020

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Re: June 24, 2020

Postby SpAce » Thu Jun 25, 2020 4:55 pm

Just a funny variant of rjamil's Strong Wing.

Code: Select all
.---------------------.-----------------.--------------.
| 45     9    *245    | *25   6    8    | 7    1   3   |
| 56     1   b*3+56-2 |  7    9  a*35+2 | 246  24  8   |
| 67     367   8      |  1    4    23   | 26   9   5   |
:---------------------+-----------------+--------------:
| 146    2     146    |  3    7    46   | 8    5   9   |
| 45679  467   4569   |  8    2    456  | 1    3   46  |
| 8      346   3456   |  456  1    9    | 24   7   246 |
:---------------------+-----------------+--------------:
| 3      8     146    |  46   5    7    | 9    24  124 |
| 1469   46    1469   |  246  3    1246 | 5    8   7   |
| 2      5     7      |  9    8    14   | 3    6   14  |
'---------------------'-----------------'--------------'

7-link mixed-type oddagon: (2)r1c3 = (2=5)r1c4 = (5=3)r2c6 = (3=2)r2c3 = (2)r1c3; using internals:

(2)r2c6 = (5|6)r2c3 => -2 r2c3; stte

or:

(2)r2c6 = (65)r2c13 => -5 r2c6; stte

Another way to see it is that a Strong Wing pattern can't contain a Y-Wing. In other words, this Y-Wing is a deadly pattern, and the same guardians prevent it:

Deadly Y-Wing: (2=5)r1c4 - (5=3)r2c6 - (3=2)r2c3 => -2 r1c3

Of course all of this is unnecessarily complicated, but so is the Strong Wing pattern itself. It's basically a dual L3-Wing, but without any extra benefits compared to using either one alone. Thus, all three of these have the same exact outcome:

Strong Wing: (2)r1c3 = (2-5)r1c4 = (5-3)r2c6 = (3-2)r2c3 = (2)r1c3 => +2 r1c3; stte
L3-Wing: (2)r1c3 = (2-5)r1c4 = (5-3)r2c6 = (3)r2c3 => -2 r2c3; stte (Phil's solution)
L3-Wing: (2)r1c3 = (2-3)r2c3 = (3-5)r2c6 = (5)r1c4 => -2 r1c4; stte

(That said, Strong Wing is a fun pattern to spot, so good job, rjamil!)

Yet another way to write it:

[(3-5)r2c6] -> (32)r21c3|(52)r1c43 => +2 r1c3; stte
-SpAce-: Show
Code: Select all
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"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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