The New Sudoku Players' Forum

[eleven]

Code: Select all

 +-------+-------+-------+
 | 1 2 . | . . . | . 8 . |
 | . . . | 7 . 9 | . . . |
 | . . . | . . . | . 6 . |
 +-------+-------+-------+
 | . 8 4 | . . . | . . . |
 | . . . | . . 2 | 9 . . |
 | . 6 . | . . . | . . 2 |
 +-------+-------+-------+
 | . . . | . . . | . . . |
 | . . 7 | . 6 . | . 4 . |
 | 9 . . | 3 . 5 | . . . |
 +-------+-------+-------+

[Mathimagics]

Might MM mean Mike Metcalf, maybe? Might MM mean me, Mathimagics?

I don't know, it's just a complete alliteration to me!

[eleven]

Sorry, saw the MM in your thread.

[Mathimagics]

And I saw your "MM" on the front board ...

Anyway, I clearly don't belong here, I just wandered in off the street

Now that I'm here, though, I'm curious - in what way is that puzzle interesting?

Cheers!
MM (not that other bloke)

[SpAce]

Now that I'm here, though, I'm curious - in what way is that puzzle interesting?

Knowing eleven, there's probably a really elegant solution hiding somewhere. This is not it

Code: Select all

.------------------.------------------------.--------------------------.
|  1    2     35   | 45     345       6     |  7      8         9      |
| g46   345  f3568 | 7     e1358      9     |  135    2         135    |
|  7    9     358  | 1258   12358    d38    |  1345   6         1345   |
:------------------+------------------------+--------------------------:
|  2    8     4    | 15     9       cn3(7)  | b16     135-7    b16-7   |
|  35+  7     1    | 6      48        2     |  9      35+       48     |
|  35+  6     9    | 1458   13458-7  m348-7 | k48    a35+1[7]   2      |
:------------------+------------------------+--------------------------:
| h46   1345  2356 | 248    2478     l478   |  13568  9         135678 |
|  8    35    7    | 9      6         1     |  2      4         35     |
|  9   i14    26   | 3      2478      5     | j168    17        1678   |
'------------------'------------------------'--------------------------'

UR(35)r56c18 using internals

Code: Select all

 7r6c8 1r6c8
       1r4c7 6r4c7
       1r4c9 6r4c9 7r4c9
                   7r4c6 3r4c6
                         3r3c6 8r3c6
                               8r2c5 8r2c3
                                     6r2c3 6r2c1
                                           6r7c1 4r7c1
                                                 4r9c2 1r9c2
             6r9c7                                     1r9c7 8r9c7
                                                             8r6c7 4r6c7
                               8r7c6             4r7c6                   7r7c6
                               8r6c6                               4r6c6 7r6c6 3r6c6
 7r4c6                                                                         3r4c6
------------------------------------------------------------------------------------
-7r4c89,
  r6c56; stte


as an awkward chain: Show

(7==1)r6c8 - (1=6*7)r4c79 - (7=3)r4c6 - (3=8^)r3c6 - r2c5 = (86)r2c31 - (6=4)r7c1 - (41|*61)r9c27|(4|^8)r7c6 = (847)r96c7,r7c6 - (4|7|^8=3)r6c6 - (3=7)r4c6 => -7 r4c89,r6c56; stte

Added. A bit simpler version:

Code: Select all

.--------------------.---------------------.------------------------.
| 1      2      35   | 45    345      6    |   7       8     9      |
| 46     345    3568 | 7     1358     9    |   135     2     135    |
| 7      9      358  | 1258  12358    38   |   1345    6     1345   |
:--------------------+---------------------+------------------------:
| 2      8      4    | 15    9        37   |  c16     c1357  167    |
| 35     7      1    | 6     48       2    |   9       35    48     |
| 35     6      9    | 1458  134578  e3478 |  d48     c1357  2      |
:--------------------+---------------------+------------------------:
| 6-4    135-4  2356 | 248   2478   f(4)78 |   13568   9     135678 |
| 8      35     7    | 9     6        1    |   2       4     35     |
| 9   ac[4]1    26   | 3     278-4    5    | bd168    b17   b1678   |
'--------------------'---------------------'------------------------'

(4=1)r9c2 - r9c789 = (1)r9c2&(16)b6p821 - (1|6=84)r96c7 - r6c6 = (4)r7c6 => -4 r7c12,r9c5; stte

[eleven]

A cheap way to solve it is by the knowledge, that M. posts the puzzles with the solution grid in lexicographical order, i.e. the first row is 1 to 9, and r2c1=4.
So you have to find another way now ...

[Cenoman]

Code: Select all

 +---------------------+-------------------------+--------------------------+
 |  1    2      35     |  45     345      6      |  7       8      9        |
 |  46   345    3568   |  7      1358     9      |g'135     2     g135      |
 |  7    9      358    |  1258   12358    38     |g'1345    6    gf(4)135   |
 +---------------------+-------------------------+--------------------------+
 |  2    8      4      |  15     9        37     |  16      1357   167      |
 |  35   7      1      |  6     d48       2      |  9       35    e48       |
 |  35   6      9      |  1458   134578   3478   |  48      1357   2        |
 +---------------------+-------------------------+--------------------------+
 |  46  a1345   2356   |  248    2478     478    |g'3568-1  9      35678-1  |
 |  8    35     7      |  9      6        1      |  2       4     g35       |
 |  9   b14     26     |  3     c2478     5      |  168     17     1678     |
 +---------------------+-------------------------+--------------------------+

(1)r7c2 = (1-4)r9c2 = r9c5 - r5c5 = r5c9 - r3c9 = [(351)r238c9 & (435)r238c7] => -1 r7c79; ste

[SpAce]

(1)r7c2 = (1-4)r9c2 = r9c5 - r5c5 = r5c9 - r3c9 = [(351)r238c9 & (435)r238c7] => -1 r7c79; ste

Very nice!

[blue]

Code: Select all

+----------------+---------------------+------------------------+
| 1   2     35   | 45    345      6    |   7      8      9      |
| 46  345   3568 | 7     1358     9    |  e135    2      135    |
| 7   9     358  | 1258  12358    38   |  e1345   6      1345   |
+----------------+---------------------+------------------------+
| 2   8     4    | 15    9        37   | df16    f1357   167    |
| 35  7     1    | 6    a48       2    |   9      35    b48     |
| 35  6     9    | 1458  134578   3478 |   48    f1357   2      |
+----------------+---------------------+------------------------+
| 46  1345  2356 | 248   2478     478  |  e13568  9     c135678 |
| 8   35    7    | 9     6        1    |   2      4      35     |
| 9  g14    26   | 3     278-4    5    | df168   f17    c1678   |
+----------------+---------------------+------------------------+

(4=8)r5c5 - r5c9 = r79c9 - (8=16)r49c7 - 1r237c7 = (Franken X-Wing: <1>c78\b6r9) - (1=4) r9c2 => -4r9c5; stte

[SpAce]

(4=8)r5c5 - r5c9 = r79c9 - (8=16)r49c7 - 1r237c7 = (Franken X-Wing: <1>c78\b6r9) - (1=4) r9c2 => -4r9c5; stte

Lovely!

[eleven]

Impressive solutions !

Code: Select all

 *--------------------------------------------------------------------------*
 |  1    2      35     |  45     345      6      |  7       8      9        |
 |  46  a345    3568   |  7      1358     9      | #135     2    d#135      |
 |  7    9      358    |  1258   12358    38     |  1345    6      4-135    |
 |---------------------+-------------------------+--------------------------|
 |  2    8      4      |  15     9        37     |  16      1357   167      |
 |  35   7      1      |  6      48       2      |  9       35     48       |
 |  35   6      9      |  1458   134578   3478   |  48      1357   2        |
 |---------------------+-------------------------+--------------------------|
 |  46   1345   2356   |  248    2478     478    |  13568   9     d135678   |
 |  8   #35     7      |  9      6        1      |  2       4    d#35       |
 |  9   b14     26     |  3      2478     5      | b168    b17    b1678     |
 *--------------------------------------------------------------------------*

#-marked cells: if r2c79,r8c9 are not 135, r2c7 and r8c9 must be both 3 or both 5, and r2c7 and r8c2 must be 3 and 5.
135r2c79,r8c9 = 35r2c7,r8c2 - (3|5=4)r2c2 - (4=678)r9c2789 - (6|7|8=135)r278c9 => -135r3c9, stte

[SpAce]

#-marked cells: if r2c79,r8c9 are not 135, r2c7 and r8c9 must be both 3 or both 5, and r2c7 and r8c2 must be 3 and 5.
135r2c79,r8c9 = 35r2c7,r8c2 - (3|5=4)r2c2 - (4=678)r9c2789 - (6|7|8=135)r278c9 => -135r3c9, stte

Didn't I say something about a "really elegant solution"? If that doesn't qualify then I don't know what does! Very cool, in more than one way! Can't say I'm surprised but I'm still awestruck

Btw, I'd probably use '==' for the first link because it's kind of derived. To avoid that, I think this might work without explanations:

(135=6|7|8)r278c9 - (6781=4)r9c7892 - (4=3|5)r2c2 - (35)r2c79,r8c2 = (15,3|13,5)r2c79,r8c9 => -135 r3c9; stte

[blue]

Nice indeed, eleven !

(135=6|7|8)r278c9 - (6781=4)r9c7892 - (4=3|5)r2c2 - (35)r2c79,r8c2 = (15,3|13,5)r2c79,r8c9 => -135 r3c9; stte

I see your mention of r8c2, but really no clear indication that r8c9 would match r2c2, and (with that) be distinct from r2c7.

Added: OK, I see ... "(3|5)r2c2 - r8c2 = r8c9" sort of does it.
I would probably still make special mention of it, though.

[SpAce]

Hi blue,

(135=6|7|8)r278c9 - (6781=4)r9c7892 - (4=3|5)r2c2 - (35)r2c79,r8c2 = (15,3|13,5)r2c79,r8c9 => -135 r3c9; stte

I see your mention of r8c2, but really no clear indication that r8c9 would match r2c2, and (with that) be distinct from r2c7.

Added: OK, I see ... "(3|5)r2c2 - r8c2 = r8c9" sort of does it.
I would probably still make special mention of it, though.

I'm glad if you think it's correct (?), after all. That said, I have no disagreement about the lack of transparency in the last link. I can easily follow the flow from left to right but it's not so easy the other way around (which is why I reversed the chain in the first place). Usually that indicates a mistake as every link should work independently and regardless of the orientation. Yet I can't see an actual mistake here (but if you do, please inform!). Unfortunately I can't really see much clearer ways to write it either.

This is the intended logic anyway, from the most explicit net to the most flattened and reduced version:

full logic: Show

Code: Select all

Iteration 1:

           (3=15)r2c79
          /
  (3)r2c2
  ||      \
  ||       (3)r8c2 = (3)r8c9
  ||
- (4)r2c2
  ||
  ||       (5=13)r2c79
  ||      /
  (5)r2c2
          \
           (5)r8c2 = (5)r8c9


Iteration 2:

  (3)r2c2 - (3)r2c79,r8c2 = (15)r2c79&(3)r8c9
  ||
- (4)r2c2
  ||
  (5)r2c2 - (5)r2c79,r8c2 = (13)r2c79&(5)r8c9


Iteration 3:

  (3)r2c2 - (3)r2c79,r8c2 = (15,3)r2c79,r8c9
  ||
- (4)r2c2
  ||
  (5)r2c2 - (5)r2c79,r8c2 = (13,5)r2c79,r8c9


Iteration 4:

- (4=3|5)r2c2 - (35)r2c79,r8c2 = (15,3|13,5)r2c79,r8c9


Iteration 5:

- (4=3|5)r2c2 - (35)r2c79,r8c2 = (135)r2c79,r8c9

Does that make sense? I chose to present Iteration 4 as a compromise between conciseness and a resemblance of clarity. Iteration 5 is obviously the shortest and the prettiest (only one small -- but significant -- deviation from eleven's original), and I think it would be technically correct too, but the last strong link requires even more mental acrobatics to see why it works. Still I think it's slightly less difficult than with the original 35r2c7,r8c2 which requires seeing the interactions within the r2c79,r8c9 group. My way avoids that, but I understand that it's not how eleven saw the logic.

[blue]

Hi SpAce,

I'm glad if you think it's correct (?), after all.
(...)
Yet I can't see an actual mistake here (but if you do, please inform!).

Correct, yes -- just difficult to follow, without a narrative to go along with it.

This is the intended logic anyway, from the most explicit net to the most flattened and reduced version:

Nice pics ! ... easy to follow the evolution.

How about one of these ?

(135=6|7|8)r278c9 - (6781=4)r9c7892 - (4)r2c2 =* ((1)r2c79 & remote pair <35>r2c79,*r2c2,r8c2,r8c9) => -135 r3c9; stte
(135=6|7|8)r278c9 - (6781=4)r9c7892 - (4)r2c2 = (remote triple, type 1: <135>r2c79,r8c9) => -135 r3c9; stte

[ I don't know if the "remote triple" term has been used before, and "type 1" is only meant to suggest the possiblity of other types existing. ]

Cheers,
Blue.