The New Sudoku Players' Forum

[tarek]

Code: Select all

+-------+-------+-------+
| . . . | 4 . 1 | . 6 . |
| 3 1 8 | . 7 . | . . 2 |
| . . . | 5 . . | . . . |
+-------+-------+-------+
| . . 1 | 3 . . | . . 6 |
| . 2 . | . . . | . 8 . |
| . . 9 | . . 2 | 5 . 1 |
+-------+-------+-------+
| . . . | 7 . 9 | . 4 . |
| 2 . . | . 5 . | . 9 . |
| . 8 . | . . . | . 1 . |
+-------+-------+-------+
...4.1.6.318.7...2...5.......13....6.2.....8...9..25.1...7.9.4.2...5..9..8.....1.


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[Leren]

Code: Select all

*------------------------------------*
| 7 59  25 | 4  238  1   | 38  6 389 |
| 3 1   8  | 9  7    6   | 4   5 2   |
| 4 69  26 | 5  238  38  | 1   7 389 |
|----------+-------------+-----------|
| 8 4   1  | 3  9    5   | 7   2 6   |
| 5 2   3  | 6  1    7   | 9   8 4   |
| 6 7   9  | 8  4    2   | 5   3 1   |
|----------+-------------+-----------|
| 1 356 56 | 7  368  9   | 2   4 38  |
| 2 36  4  | 1  5   d8-3 |c368 9 7   |
| 9 8   7  | 2 a36   4   |b36  1 5   |
*------------------------------------*

(3) r9c5 = (3-6) r9c7 = (6-8) r8c7 = (8) r8c6 => - 3 r8c6; stte

Leren

[tarek]

7 minutes

[pjb]

Code: Select all

 7       59      25     | 4      238    1      | 38     6      389   
 3       1       8      | 9      7      6      | 4      5      2     
 4       69      26     | 5      238    38     | 1      7      389   
------------------------+----------------------+---------------------
 8       4       1      | 3      9      5      | 7      2      6     
 5       2       3      | 6      1      7      | 9      8      4     
 6       7       9      | 8      4      2      | 5      3      1     
------------------------+----------------------+---------------------
 1      a356     56     | 7      368    9      | 2      4     d38     
 2      b36      4      | 1      5      38     |c368    9      7     
 9       8       7      | 2      36     4      | 36     1      5     


(3)r7c2 = (3-6)r8c2 = (6-8)r8c7 = r7c9 => -3 r7c9; stte

Phil

[rjamil]

Code: Select all

 +------------+---------------+---------------+
 | 7  59   25 | 4  238   1    | 38    6  389  |
 | 3  1    8  | 9  7     6    | 4     5  2    |
 | 4  69   26 | 5  238   38   | 1     7  389  |
 +------------+---------------+---------------+
 | 8  4    1  | 3  9     5    | 7     2  6    |
 | 5  2    3  | 6  1     7    | 9     8  4    |
 | 6  7    9  | 8  4     2    | 5     3  1    |
 +------------+---------------+---------------+
 | 1  356  56 | 7  36-8  9    | 2     4  (38) |
 | 2  36   4  | 1  5     (38) | 36-8  9  7    |
 | 9  8    7  | 2  (3)6  4    | (3)6  1  5    |
 +------------+---------------+---------------+

W-Wing: 38 @ r7c9 r8c6 SL Row 9 between 3 @ r9c5 and 3 @ r9c7 => -8 @ r7c5 r8c7; stte

R. Jamil

[SteveG48]

Code: Select all

 *---------------------------------------------------*
 | 7   d59   25   | 4    238  1    |  38   6    38-9 |
 | 3    1    8    | 9    7    6    |  4    5    2    |
 | 4    6-9  26   | 5    238 a38   |  1    7   a389  |
 *----------------+----------------+-----------------|
 | 8    4    1    | 3    9    5    |  7    2    6    |
 | 5    2    3    | 6    1    7    |  9    8    4    |
 | 6    7    9    | 8    4    2    |  5    3    1    |
 *----------------+----------------+-----------------|
 | 1   d356  56   | 7  bc368  9    |  2    4   a38   |
 | 2   d36   4    | 1    5   a38   |bc368  9    7    |
 | 9    8    7    | 2    36   4    |  36   1    5    |
 *---------------------------------------------------*


[9=RP(3/8)r3c69,r7c9,r8c6] - (3|8)r7c5,r8c7 = 6r7c5&r8c6 - (6=359)r178c2 => -9 r1c9,r3c2 ; stte

[SpAce]

Inspired by Steve's cool solution.

Code: Select all

.------------.------------------.----------------.
| 7  59   25 | 4    238     1   | 38   6    389  |
| 3  1    8  | 9    7       6   | 4    5    2    |
| 4  69   26 | 5    238   ac38* | 1    7    9-38 |
:------------+------------------+----------------:
| 8  4    1  | 3    9       5   | 7    2    6    |
| 5  2    3  | 6    1       7   | 9    8    4    |
| 6  7    9  | 8    4       2   | 5    3    1    |
:------------+------------------+----------------:
| 1  356  56 | 7  bc38#6*   9   | 2    4  ac38*  |
| 2  36   4  | 1    5     bc38* | 368  9    7    |
| 9  8    7  | 2    36      4   | 36   1    5    |
'------------'------------------'----------------'

(3,8)r3c6,r7c9 = (38-6)b8p26 = RP(38)r38c6,r7c59 => -38 r3c9; stte

[eleven]

(3,8)r3c6,r7c9 = (38-6)b8p26 = RP(38)r38c6,r7c59 => -38 r3c9; stte

I can't see the link 38b8p26 = (3,8)r3c6,r7c9.

[SpAce]

(3,8)r3c6,r7c9 = (38-6)b8p26 = RP(38)r38c6,r7c59 => -38 r3c9; stte

I can't see the link 38b8p26 = (3,8)r3c6,r7c9.

I'm not exactly surprised Yeah, I know it's not the most obvious link, especially in that orientation, but just this one time I chose to sacrifice clarity for brevity and aesthetics. Shocking, I know.

Anyway, the way I arrived at that was by simplifying this:

(3,8)r3c6,r7c9 = (3,8)b8p62|(8,3)b8p26 - 6b8p2 = RP(38)r38c6,r7c59

You agree with that, I hope? I just combined the ORed terms because they were equal, and dropped the comma because the following weak link wasn't interested in the exact cells of the digits. I knew those simplifications made the logic harder to see (for me too), especially reversed, but I guess I'm a beauty before brains kind of guy. I believe it's correct anyhow unless someone proves otherwise. My logic for the reversal is that there's only one way 38b8p26 can be false: 6b8p2 is true, which forces (8,3)r83c6 and 8r7c9, i.e. (3,8)r3c6,r7c9.

The normal left-to-right orientation is a bit more straight-forward to understand, I think. Who told to read if from right-to-left anyway? The rule is that an AIC must be correct both ways (well, it can only be correct both ways or not at all), but no one said it must be understandable both ways

[eleven]

(3,8)r3c6,r7c9 = (3,8)b8p62|(8,3)b8p26 - 6b8p2 = RP(38)r38c6,r7c59

You agree with that, I hope?

No, if i look at the 4 cells, and 3c6,r7c9 is not 3,8, but 3,3, then b8p6 is 8 and b8p2 is 6.

[SpAce]

(3,8)r3c6,r7c9 = (3,8)b8p62|(8,3)b8p26 - 6b8p2 = RP(38)r38c6,r7c59

You agree with that, I hope?

No, if i look at the 4 cells, and 3c6,r7c9 is not 3,8, but 3,3, then b8p6 is 8 and b8p2 is 6.

You shouldn't give me heart attacks first thing in the morning! The ripples in the Force betrayed the anticipation of my haters rooting for you to embarrass me

(As if I would be embarrassed of something I'd consider a great learning opportunity! I actually hope you're right and there's something I failed (and still fail) to see.)

My brain wasn't firing on all three cylinders when I wrote the chain, but I still can't see the mistake. As far as I see, you're (briefly) right if you only consider the four cases of the digit distribution in the two cells r3c6 and r7c9:

Code: Select all

(3,8 = 8,3 | 3,3 | 8,8) r3c6,r7c9

Of those the (3,3) case you mentioned does indeed imply (6,8)b8p26, but it can just as well imply (8,3) or even more simply (8,8) or (8,-) in the same cells, depending on the way you look at it. In fact, you could make it imply that the earth is flat if you wanted to. That's the wonderful nature of false cases. Thus, even if I'd used your approach, I could have dismissed (3,3) as false due to the obvious contradictions (8,8) or (8,-) which I'd seen first. Besides, (6,8)b8p26 implies (3,8)r3c6,r7c9 so it wouldn't be a bad case for a (slightly different) verity proof either.

That's not what I did, however, nor do I see any reason to. To break the (3,8)r3c6,r7c9 it's simpler to use the two external spoilers 3r8c6 and 8r7c5, which leaves just the previously mentioned two cases (blending into one) to consider:

Code: Select all

(3,8)r3c6,r7c9 = 3r8c6|8r7c5 <-> 3b8p6|8b8p2

Since 3b8p6 -> 8b8p2 and 8b8p2 -> 3b8p6, we have (3,8)b8p62 either way.

Do you now agree? Or am I really blind to something?

--
Another way to see the logic:

Code: Select all

RP(38)r38c6,r7c59 = (68)b8p26 - (8)r3c6|r7c5 = (3,8)r3c6,r7c9 => -38 r3c9; stte

...or the same through a bivalue oddagon:

Code: Select all

(9)r3c9 =BV_ODGN= (68)b8p26 - (8)r7c5|r3c6 = (3,8)r3c6,r7c9 => -38 r3c9; stte

Or explicitly with a slightly different route (no 6r7c5 involved):

Code: Select all

(3,8)r3c6,r7c9 = 3b8p6|8b8p2 - 8b8p6 = (3,8)b8p62 - 3r3c6|8r7c9 = (8,3)r3c6,r7c9 => -38 r3c9

...or the same even more explicitly (',' in place of '&' for readability):

Code: Select all

3r3c6,8r7c9 = 3r8c6|8r7c5 - 8r8c6 = 3r8c6,8r7c5 - 3r3c6|8r7c9 = 8r3c6,3r7c9 => -38 r3c9


Take your pick if you don't like the original. (But if you still think it's actually incorrect, I'd love to learn why.)

[eleven]

SpAce,

i do not take part in your notation games.
When i see a solution in whatever notation, i try to find out the logic contained in it, and as far as i remember i always succeeded, if the solution was correct. Not in this case.

You mangled 3 cases into one AIC style link, and when i tried to verify the first one, it turned out to be wrong. Now i see, that it would be right, if i had used the strong links for 8 instead of the candidates links in the cells.
The conclusion is, that the link is both right and wrong, which i cannot accept.

[SteveG48]

I can't see the link 38b8p26 = (3,8)r3c6,r7c9.

I guess I don't see the problem. If 3 and 8 are not both true in b8p26, then b8p2 cannot be 8. In that case, both b8p6 and r7c9 would have to be 8 and r3c6 would have to be 3. Not so?

An assumption of (3,3)r3c6,r7c9 is not viable, since it quickly eliminates 8 from r7.

[eleven]

... and it quickly eliminates 38 from r7c5, proving the link wrong.
If the used links are not listed, you can see it this or that way.

In normal AIC each used link is part of the notation, being more strict here than forcing chains, which often are shortened, but never in such an ambiguous way.

[Sudtyro2]

Code: Select all

+---------------+----------------+---------------+
| 7   59    25  | 4   238    1   |  38   6   389 |
| 3   1     8   | 9   7      6   |  4    5   2   |
| 4   69    26  | 5   238    38  |  1    7   389 |
+---------------+----------------+---------------+
| 8   4     1   | 3   9      5   |  7    2   6   |
| 5   2     3   | 6   1      7   |  9    8   4   |
| 6   7     9   | 8   4      2   |  5    3   1   |
+---------------+----------------+---------------+
| 1  *36+5  56  | 7  *3+8-6  9   |  2    4   38  |
| 2  *36    4   | 1   5      38  | *36+8 9   7   |
| 9   8     7   | 2  *36     4   | *36   1   5   |
+---------------+----------------+---------------+

Something a little simpler, perhaps...
DP(36), using internals.
(5)r7c2 - (5=6)r7c3
(8)r7c5
(8)r8c7 - r7c9 = (8)r7c5
=> -6 r7c5; stte

SteveC