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[tarek]

2 steps with basics from me

Code: Select all

+-------+-------+-------+
| . . 9 | 5 . 6 | . . . |
| 1 . . | . 7 8 | . . . |
| 8 5 . | . . . | . . . |
+-------+-------+-------+
| . . . | . 3 . | . 7 6 |
| . 7 . | . . 4 | . 9 . |
| 3 . 1 | . . . | . . 4 |
+-------+-------+-------+
| . 3 . | 7 . . | . . 9 |
| 2 . 7 | . 4 . | 6 . . |
| . 9 . | 2 . . | 4 1 . |
+-------+-------+-------+
..95.6...1...78...85...........3..76.7...4.9.3.1.....4.3.7....92.7.4.6...9.2..41.


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[SpAce]

Code: Select all

.-----------------------.--------------------.--------------------.
|  7    24      9       |   5     12     6   | 1238   2348  1238  |
|  1    24-6   a34[+6]2 |  a34+   7      8   | 9      2456  25    |
|  8    5      a34[+6]  |  a34+   129    129 | 7      46    12    |
:-----------------------+--------------------+--------------------:
|  9    248     245     |   18    3     d25  | 1258   7     6     |
| b56   7      b25-6    |  c168  c258    4   | 12358  9     12358 |
|  3   f2(6)8   1       | df689  d2589   7   | 258    258   4     |
:-----------------------+--------------------+--------------------:
|  4    3       568     |   7     1568   15  | 258    258   9     |
|  2    1       7       |  e89    4     e59  | 6      358   358   |
|  56   9       568     |   2     568    3   | 4      1     7     |
'-----------------------'--------------------'--------------------'

(6=UR=2)r23c34 - (2=56)r5c13 - r5c45 = (695)b5p783 - (59)r8c64 = (96)r6c42 => -6 r2c2,r5c3; stte

8x8 TM: Show

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 6r23c3 2r2c3
        2r5c3 56r5c13
              6r5c4   6r6c4
                      9r6c4 9r6c5
              5r5c5         5r6c5 5r4c6
                                  5r8c6 9r8c6
                                        9r8c4 9r6c4
 6r6c2                                        6r6c4
---------------------------------------------------
-6r2c2
-6r5c3

[eleven]

Code: Select all

 *--------------------------------------------------------------------*
 |  7    24    9      |  5     12     6     |  1238    2348   1238    |
 |  1    246   2346   |  34    7      8     |  9       2456   25      |
 |  8    5     346    |  34    129    129   |  7       46     12      |
 |--------------------+---------------------+-------------------------|
 |  9    248   245    | b18    3     b25    |  1258    7      6       |
 | d56   7     256    | b168  c258    4     |  12358   9      12358   |
 |  3    268   1      | b689   2589   7     |  258     258    4       |
 |--------------------+---------------------+-------------------------|
 |  4    3    #568    |  7    #1568   15    |  258     258    9       |
 |  2    1     7      | a89    4     a59    |  6       358    358     |
 | e56   9    #568    |  2    #568    3     |  4       1      7       |
 *--------------------------------------------------------------------*

UR 68 r79c35: 6r9c1 = 8r8c4
8r8c4 = 95r8c46 - (9|5=1682)b5p1473 - (2|8=5)r5c5 - r5c1 = (5-6)r9c1 == 8r8c4 => 8r8c4, stte

[SpAce]

8r8c4 = 95r8c46 - (9|5=1682)b5p1473 - (2|8=5)r5c5 - r5c1 = (5-6)r9c1 == 8r8c4 => 8r8c4, stte

The same as a "riddle" (just because we know how much you love them):

8r8c4 == 6,5r95c1 - r5c5 = 59r48c6|r6c54 => -9r8c4; stte

[eleven]

8r8c4 == 6,5r95c1 - r5c5 = 59r48c6|r6c54 => -9r8c4; stte

No problem with that one.

[SpAce]

8r8c4 == 6,5r95c1 - r5c5 = 59r48c6|r6c54 => -9r8c4; stte

No problem with that one.

Didn't think so. In this case we can probably both agree that it's actually easier to read than the longer version. Sometimes it pays off even in terms of clarity and simplicity to look for a shorter notation. Besides, in that form your solution is easier to compare with mine because both are probably as lean as possible.

That way it's easy to see that yours is intrinsically way simpler (better), which is not (at all) obvious with your routing and notation. If anything, it's more complicated. Originally both are 9x9 matrices (subsets fully unfolded), mine a PM (simpler) and yours a BTM. However, mine doesn't (probably) get any simpler than that, while yours is easily reduced to a much simpler 5x5 PM.

my solution 9x9 PM: Show

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 6r23c3 2r2c3
        2r5c3 5r5c3 6r5c3
              5r5c1 6r5c1
                    6r5c4 6r6c4
                          9r6c4 9r6c5
              5r5c5             5r6c5 5r4c6
                                      5r8c6 9r8c6
                                            9r8c4 9r6c4
 6r6c2                                            6r6c4
-------------------------------------------------------
-6r2c2
-6r5c3

your solution 9x9 BTM: Show

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 8r8c4 9r8c4
       9r8c6 5r8c6
             5r4c6 2r4c6
       9r6c4             6r6c4 8r6c4
                         6r5c4 8r5c4 1r5c4
                               8r4c4 1r4c4
                   2r5c5       8r5c5       5r5c5
                                           5r5c1 6r5c1
 8r8c4                                           6r9c1
------------------------------------------------------
+8r8c4

your solution with my notation 5x5 PM: Show

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 9r6c4 9r6c5
 9r8c6       5r8c6
       5r6c5 5r4c6 5r5c5
                   5r5c1 6r5c1
 8r8c4                   6r9c1
------------------------------
-9r8c4

Then again, what do I know.

--
Edit. Changed the matrix types to what I think is probably more correct. Cenoman would know exactly.