July 23, 2020

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July 23, 2020

Postby tarek » Thu Jul 23, 2020 10:59 am

Code: Select all
+-------+-------+-------+
| . . 3 | . 4 . | 2 5 . |
| 8 . . | . . . | 1 . 4 |
| . . . | . . . | . 9 8 |
+-------+-------+-------+
| 3 . . | 9 . . | . . . |
| . . . | . . . | . . 6 |
| 2 8 1 | . . 6 | . . . |
+-------+-------+-------+
| . 1 7 | 2 . . | . . 9 |
| . . 9 | 3 . . | . . . |
| . . . | 5 . 4 | . 2 . |
+-------+-------+-------+
..3.4.25.8.....1.4.......983..9.............6281..6....172....9..93........5.4.2.

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Re: July 23, 2020

Postby yzfwsf » Thu Jul 23, 2020 11:35 am

Code: Select all
.-------------.---------------.--------------.
| 1  6    3   | 8    4    9   | 2    5     7 |
| 8  9    25  | 67   237  235 | 1    36    4 |
| 7  45   245 | a16  123  235 | 3-6   9    8 |
:-------------+---------------+--------------:
| 3  457  6   | 9    8    17  | 45   147   2 |
| 9  457  45  | b147 23   23  | 458  c1478 6 |
| 2  8    1   | 47   5    6   | 9    47    3 |
:-------------+---------------+--------------:
| 5  1    7   | 2    6    8   | 34   34    9 |
| 4  2    9   | 3    17   17  | e68  d68   5 |
| 6  3    8   | 5    9    4   | 7    2     1 |
'-------------'---------------'--------------'

(6=1)r3c4-r5c4=(1-8)r5c8=(8-6)r8c8=6r8c7 =>-6r3c7;stte
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Re: July 23, 2020

Postby SpAce » Thu Jul 23, 2020 12:56 pm

Code: Select all
    A  B    C      D    E    F      G     H      I
  .-------------.----------------.-----------------.
a | 1  6    3   |  8    4    9   |  2     5      7 |
b | 8  9    25  |  67   237  235 |  1    c36     4 |
c | 7  45   245 | a16   123  235 | b36    9      8 |
  :-------------+----------------+-----------------:
d | 3  457  6   |  9    8    17  |  45    147    2 |
e | 9  457  45  | a147  23   23  |  458  d478-1  6 |
f | 2  8    1   |  47   5    6   |  9     47     3 |
  :-------------+----------------+-----------------:
g | 5  1    7   |  2    6    8   |  34    34     9 |
h | 4  2    9   |  3    17   17  |  68   d68     5 |
i | 6  3    8   |  5    9    4   |  7     2      1 |
  '-------------'----------------'-----------------'

(16)ecD = cG - bH = (68)heH => -1eH; stte

(16)r53c4 = r3c7 - r2c8 = (68)r85c8 => -1 r5c8; stte

uncompressed aIrZ + rYcX: Show
(1)eD = (1-6)cD = cG - bH = (6-8)hH = (8)eH => -1eH; stte

(1)r5c4 = (1-6)r3c4 = r3c7 - r2c8 = (6-8)r8c8 = (8)r5c8 => -1 r5c8; 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: July 23, 2020

Postby Ajò Dimonios » Thu Jul 23, 2020 2:16 pm

Code: Select all
+-----------+-------------+------------+
| 1 6   3   | 8   4   9   | 2   5    7 |
| 8 9   25  | 67  237 235 | 1   36   4 |
| 7 45  245 | 16  123 235 | 36  9    8 |
+-----------+-------------+------------+
| 3 457 6   | 9   8   17  | 45  147  2 |
| 9 457 45  | 147 23  23  | 458 1478 6 |
| 2 8   1   | 47  5   6   | 9   47   3 |
+-----------+-------------+------------+
| 5 1   7   | 2   6   8   | 34  34   9 |
| 4 2   9   | 3   17  17  | 68  68   5 |
| 6 3   8   | 5   9   4   | 7   2    1 |
+-----------+-------------+------------+



7r8c5=7r2c5-(7=6) r2c4-6r2c8=(6-8)r8c8=(8-1)r5c8=1r5c4-1r3c4=1r3c5-(1=7)r8c5=>+7r8c5=>stte
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Re: July 23, 2020

Postby SpAce » Thu Jul 23, 2020 2:54 pm

Just to showcase some extra capabilities of the aIrZ-coordinates...

My previous solution in the nc-space:

Code: Select all
    A    B    C      D    E    F      G     H     I
  .---------------.----------------.-----------------.
1 | a    g    f   | Ace   ch   dh  |  b     d-e   i  |
2 | f    h    bc  |  g    bce  bce |  c     b     d  |
3 | d    i    a   |  h    bce  bce |  cg    bg    f  |
4 | h    cde  ce  |  ef   a    i   |  deg   defg  b  |
5 | g    cde  bce |  i    f    bc  |  de    a     h  |
6 | i    a    d   | Abc   g    f   |  ch   Bbh    e  |
7 | c    de   g   |  bef  bh   dh  |  i     def   a  |
8 | b    f    i   |  a    d    g   |  eh   Beh    c  |
9 | e    b    h   |  d    i    a   |  f     c     g  |
  '---------------.----------------.-----------------'

(e=cb)16D - (bh=e)68H => -e1H; stte

That might be the shortest solution we'll see today. The same as a simple xy-chain:

(e=c)1D - (c=b)6D - (b=h)6H - (h=e)8H => -e1H; stte

It's not quite so nice in the rn-space:

Code: Select all
     1    2    3    4      5     6    7     8    9
  .-------------------------------------------------.
a |  A    G    C    E      H     B    I     D    F  |
b |  G    CEF  EFH  I      CF    DH   DE    A    B  |
c | bDE   CEF  EFG  BC     BCF  cDG   A     I    H  |
  :-------------------------------------------------:
d |  FH   I    A    BGH    BG    C    BFH   E    D  |
e | aD-H  EF   EF   BCDGH  BCG   I    BDH  fGH   A  |
f |  C    A    I    DH     E     F    DH    B    G  |
  :-------------------------------------------------:
g |  B    D    GH   GH     A     E    C     F    I  |
h |  EF   B    D    A      I    dGH   EF   eGH   C  |
i |  I    H    B    F      D     A    G     C    E  |
  '-------------------------------------------------'

(D)e1 = c1 - (D=G)c6 - h6 = h8 - (G=H)e8 => -He1; stte

...or a bit compressed:

(D)e1 = (DG)c16 - h6 = (G,H)he8 => -He1; stte

--

The point is that the aIrZ-system works very smoothly and unambiguously in any solving space (including various box-spaces; not shown) because each coordinate (n, r, c, b, p) has a different set of symbols. Of course very few people ever solve in anything other than the rc-space, but still. (It's actually quite fun and educating every once in a while.)
-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: July 23, 2020

Postby Ngisa » Thu Jul 23, 2020 4:38 pm

Code: Select all
+-----------------+-------------------+------------------+
| 1    6      3   | 8      4      9   | 2      5       7 |
| 8    9      25  |e67     237    235 | 1     d36      4 |
| 7    45     245 | 16     123    235 | 36     9       8 |
+-----------------+-------------------+------------------+
| 3    457    6   | 9      8     g7-1 | 45    a147     2 |
| 9    457    45  |f147    23     23  | 458   b1478    6 |
| 2    8      1   |f47     5      6   | 9      47      3 |
+-----------------+-------------------+------------------+
| 5    1      7   | 2      6      8   | 34     34      9 |
| 4    2      9   | 3      17     17  | 68    c68      5 |
| 6    3      8   | 5      9      4   | 7      2       1 |
+-----------------+-------------------+------------------+

(1)r4c8 = (1-8)r5c8 = (8-6)r8c8 = r2c8 - (6=7)r2c4 - r56c4 = (7)r4c6 => - 1r4c6; stte

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Re: July 23, 2020

Postby SteveG48 » Thu Jul 23, 2020 5:00 pm

Code: Select all
 *-----------------------------------------------------------*
 | 1     6     3     | 8     4     9     | 2     5     7     |
 | 8     9     25    | 67    237   235   | 1     36    4     |
 | 7     45    245   |c16    123   235   |d36    9     8     |
 *-------------------+-------------------+-------------------|
 | 3     457   6     | 9     8    b17    | 5-4  a147   2     |
 | 9     457   45    |c147   23    23    | 58-4  1478  6     |
 | 2     8     1     |c47    5     6     | 9    a47    3     |
 *-------------------+-------------------+-------------------|
 | 5     1     7     | 2     6     8     |d34    3-4   9     |
 | 4     2     9     | 3     17    17    | 68    68    5     |
 | 6     3     8     | 5     9     4     | 7     2     1     |
 *-----------------------------------------------------------*


(4=71)r46c8 - (1=7)r4c6 - (7=146)r356c4 - (6=34)r37c7 => -4 r45c7,r7c8 ; stte

(4=71)dfH - (1=7)dF - (7=146)cefD - (6=34)cgG => -4 deG,gH ; stte

The proposed coordinate system clearly saves a bit of space (no pun intended). My first problem with it, naturally, is figuring out which letters to use. Familiarity might
help there. The second problem is that I sometime have trouble distinguishing between i and I in the forum default font.
Steve
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Re: July 23, 2020

Postby Cenoman » Thu Jul 23, 2020 6:56 pm

Code: Select all
 +-------------------+--------------------+--------------------+
 |  1    6     3     |  8     4     9     |  2     5      7    |
 |  8    9     25    | z67    237   235   |  1    y36     4    |
 |  7    45    245   |  16    123   235   |  36    9      8    |
 +-------------------+--------------------+--------------------+
 |  3  wA457*  6     |  9     8     17    |wB45  xa147*   2    |
 |  9   v457*  45    |za147*  23    23    | C458  C478-1  6    |
 |  2    8     1     | z47*   5     6     |  9     47*    3    |
 +-------------------+--------------------+--------------------+
 |  5    1     7     |  2     6     8     |  34   y34     9    |
 |  4    2     9     |  3     17    17    |  68    68     5    |
 |  6    3     8     |  5     9     4     |  7     2      1    |
 +-------------------+--------------------+--------------------+

DP(47)r456c248 using internals
(1)r4c8,r5c4
(5)r4c2 - r4c7 = (58)r5c78
(5-7)r5c2 = (7-54)r4c27 = r4c8 - (4=36)r27c8 - (6=471)r256c4
=> -1 r5c8; ste
Edit: corrected typo (Thanks SteveC !)
Last edited by Cenoman on Fri Jul 24, 2020 8:45 pm, edited 1 time in total.
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Re: July 23, 2020

Postby SpAce » Fri Jul 24, 2020 6:53 am

Hi Steve,

SteveG48 wrote:(4=71)dfH - (1=7)dF - (7=146)cefD - (6=34)cgG => -4 deG,gH ; stte

Thanks for trying it out!

The proposed coordinate system clearly saves a bit of space.

Yes, and the longer the chain the more it saves. In some cases the savings are also slightly larger if (bi)local links are favored over (bi)value links. For example, your ALS-chain above saves 16%, but if it's written with mixed links (all other things being equal), it saves 18% even though the starting chain is already shorter. The absolute saving is the same 12 characters:

Code: Select all
77: (4=71)r46c8 - (1=7)r4c6 - (7=146)r356c4 - (6=34)r37c7 => -4 r45c7,r7c8 ; stte
65: (4=71)dfH - (1=7)dF - (7=146)cefD - (6=34)cgG => -4 deG,gH ; stte

68: (4=71)r46c8 - r4c6 = (16)r35c4 - (6=34)r37c7 => -4 r45c7,r7c8 ; stte
56: (4=71)dfH - dF = (16)ceD - (6=34)cgG => -4 deG,gH ; stte

(no pun intended)

Well, saving 'space' is trivial compared to saving 'SpAce'. Some souls are beyond redemption :D

My first problem with it, naturally, is figuring out which letters to use. Familiarity might help there.

There's a definite learning curve, but in my short experience it's not overwhelming. It takes a bit of practice but it's already starting to feel natural for me. However, before I get too comfy with it, I guess the choice of the letter sets would need to be reconsidered:

The second problem is that I sometime have trouble distinguishing between i and I in the forum default font.

Good of you to mention that. I haven't noticed that particular problem myself, but the 'I' is definitely a bit of a problem child with the forum font -- unless put in a CODE-block. That's why some systems have replaced it with 'j/J' or 'k/K'. I didn't go that route (not yet at least) because I wanted to keep things easy to remember. That's why I simply chose the first 9 and the last 9 letters in the alphabet, even though both sets have some issues.

Another reason was that if I really wanted to maximize readability, I don't think dropping the 'I' would be enough. For example, I think 'B' is an even bigger problem if next to an '8'. Mostly my system avoids those problems because digits aren't normally placed next to uppercase letters, but sometimes (like in the nc-space, or with alien fishes) it's unavoidable. Thus, it would be best to avoid all ambiguously shaped letters that can be confused with digits or other letters. For example, in hand-writing 'g' and '9' look very similar, and so do 'G' and '6', so that's another problem letter. Also, 'u' and 'v' might look a bit similar at first glance, and even 'A' and '4', though I guess they're minor problems. I don't particularly like 'w/W' either, but it's for different reasons. For one, it's a wide character in a non-fixed font, and even more importantly, it's a three-syllable word when pronounced, which is annoying when reading coordinates even in your head.

So, I'm definitely open for suggestions, if someone has better ideas for a set (or rather, two sets) of letters to use. For your problem with the 'i' vs 'I' even the normal NrC-ordering doesn't help, because they're routinely placed next to each other. The simplest route would be to replace 'i/I' with 'j/J' or 'k/K', but a more comprehensive readability-optimization could get quite complicated and difficult to remember. Since readability is a major goal for me, I'm of course open for all possibilities, as long as they can be relatively easily remembered (for example, if the letters form a nice mnemonic then even strict alphabetical order isn't a must).

PS. Cenoman, I'm also very interested in your opinion, as you probably have the most experience with different coordinate systems. Have you seen any before that use letters for both rows and columns? Personally I think it's far superior to the common ones that use letters only for one coordinate, because it allows unambiguous addressing of any coordinate without further qualifiers and leaves the digits for the n-coordinate only. Also, have you seen any that can address box-coordinates the same way? While that complicates things by having to remember 18 letters instead of 9, I think it's quite essential for box-based subsets and fishes. (Another possibility I considered was an escape mechanism that would allow to use the same letters for boxes and positions as for rows and columns, but it would have other complications.)
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