The New Sudoku Players' Forum

[tarek]

Code: Select all

+-------+-------+-------+
| . 9 7 | . . . | . . . |
| . 3 . | 2 . . | . . . |
| 8 2 . | . 5 3 | . . . |
+-------+-------+-------+
| . 1 8 | . . 4 | . . 3 |
| 3 . . | . . . | . . 8 |
| 2 . . | 1 . . | 7 4 . |
+-------+-------+-------+
| . . . | 9 1 . | . 6 5 |
| . . . | . . 2 | . 1 . |
| . . . | . . . | 8 7 . |
+-------+-------+-------+
.97.......3.2.....82..53....18..4..33.......82..1..74....91..65.....2.1.......87.


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[SteveG48]

Code: Select all

 *-------------------------------------------------------------*
 | b156   9     7     |  468   68    16    |b2456  3    a1246  |
 |  156   3     1456  |  2     79    169   | 456   8     1467  |
 |  8     2     146   |  467   5     3     | 46    9     1467  |
 *--------------------+--------------------+-------------------|
 |  7     1     8     |hi56    29    4     | 69    25    3     |
 |  3     4    f69    | g567   279  g569   | 1     25    8     |
 |  2   eg56   f569   |  1     3     8     | 7     4     69    |
 *--------------------+--------------------+-------------------|
 |  4     8     23    |  9     1     7     | 23    6     5     |
 |cj569   7     356   | j568  j68    2     | 349   1     49    |
 |bk19 dhi56  bk12    |  3     4     56    | 8     7    b2-9   |
 *-------------------------------------------------------------*


2r1c9 = ((25)r1c17)&((219)r9c139) - (5|9=6)r8c1 - r9c2 = r6c2 - r56c3 = (6r5c46)&(6r6c2) - 6r4c4,r9c2 = (5r9c2)&(5r4c5) - (5=689)r8c145 - (9=12)r9c13 => -2 r9c9 ; stte

Or this one is actually longer, but I think it's a bit easier to follow:

Code: Select all

 *-----------------------------------------------------------*
 |a156   9     7     | 468   68    16    | 2456  3    k1246  |
 |a156   3     1456  | 2    h79   g169   | 456   8   hk1467  |
 | 8     2     46-1  | 467   5     3     | 46    9  ijL1467  |
 *-------------------+-------------------+-------------------|
 | 7     1     8     | 56    29    4     |c69    25    3     |
 | 3     4    e69    | 567   279  f569   | 1     25    8     |
 | 2    d56   d569   | 1     3     8     | 7     4   cj69    |
 *-------------------+-------------------+-------------------|
 | 4     8     23    | 9     1     7     | 23    6     5     |
 |a569   7     356   | 568   68    2     |b349   1    j49    |
 | 19   e56  kl12    | 3     4    f56    | 8     7    j29    |
 *-----------------------------------------------------------*


(1=569)r128c1 - 9r8c7 = (9,6)b6p19 - 6r6c23 = (6r5c3)&(6r9c2) - (6=59)r59c6 - 9r2c6 = (97)r2c59 - 7r3c9 = 1r3c9|(4692)r3689c9 - (1r12c9)&(2r9c3) = 1r3c9,r9c2 => -1 r3c3 ; stte

[eleven]

Code: Select all

 *---------------------------------------------------------------*
 | c16+5  9    7      |  468  c6+8  b16    |  2456   3   b24+16  |
 |  156   3    1456   |  2     79    169   |  456    8    1467   |
 |  8     2    146    |  467   5     3     |  46     9    1467   |
 |--------------------+--------------------+---------------------|
 |  7     1    8      |  56    29    4     |  69     25   3      |
 |  3     4    69     |  567   279   569   |  1      25   8      |
 |  2     56   569    |  1     3     8     |  7      4    69     |
 |--------------------+--------------------+---------------------|
 |  4     8    23     |  9     1     7     |  23     6    5      |
 | d5+69  7    356    |  568  d8+6   2     |  34-9   1   a49     |
 |  19    56   12     |  3     4     56    |  8      7   a29     |
 *---------------------------------------------------------------*

(9=42)r89c9 - (2|4=16)r1c69 - (1|6=58)r1c15 - (5|8=69)r8c51 => -9r8c7, stte

[Ajò Dimonios]

Code: Select all

+-------------+--------------+--------------+
| 156 9  7    | 468 68  146  | 2456 3  1246 |
| 156 3  1456 | 2   79  1469 | 456  8  1467 |
| 8   2  146  | 467 5   3    | 46   9  1467 |
+-------------+--------------+--------------+
| 7   1  8    | 456 29  4569 | 69   25 3    |
| 3   4  569  | 567 279 569  | 1    25 8    |
| 2   56 569  | 1   3   8    | 7    4  69   |
+-------------+--------------+--------------+
| 4   8  23   | 9   1   7    | 23   6  5    |
| 569 7  356  | 568 68  2    | 349  1  49   |
| 19  56 12   | 3   4   56   | 8    7  29   |
+-------------+--------------+--------------+


3r8c7=>Stte
1r3c9=>Stte

3r8c7=r8c3-(3=2)r7c3-(2=1)r9c3-r3c3=1r3c9=>3r8c7=1r3c9=>or +3r8c7=>stte; or+1r3c9=>stte;or (+3r8c7 and +1r3c9)=>stte.

[SpAce]

Code: Select all

.------------------.----------------.------------------.
| f156   9    7    | 468   68   16  | e2456  3    1246 |
|  156   3    1456 | 2    f79   169 |  456   8   f1467 |
|  8     2   d146  | 467   5    3   |  46    9   e1467 |
:------------------+----------------+------------------:
|  7     1    8    | 56    2-9  4   | a69    25   3    |
|  3     4    69   | 567   279  569 |  1     25   8    |
|  2     56   569  | 1     3    8   |  7     4    69   |
:------------------+----------------+------------------:
|  4     8    23   | 9     1    7   | d23    6    5    |
| a69-5  7    356  | 568   68   2   | b349   1   b49   |
|  19    56  c12   | 3     4    56  |  8     7   c29   |
'------------------'----------------'------------------'

(9,9)r4c7,r8c1 = r8c79 - (9=21)r9c93 - (2|1)r7c7,r3c3 = (21-5|7)b3p19 = (579)r1c1,r2c95 => -5 r8c1, -9 r4c5; stte

[SpAce]

(9=42)r89c9 - (2|4=16)r1c69 - (1|6=58)r1c15 - (5|8=69)r8c51 => -9r8c7, stte

That's the most beautiful chain I've seen in a long time. Unfortunately the elimination is not stte (or even btte). Easy to finish, though:

Code: Select all

.-----------------.----------.-------------.
| a56+1  9   7    | 4  8  16 |  25  3   12 |
| b16+5  3  a45+1 | 2  9  16 | b45  8   7  |
|  8     2   4-1  | 7  5  3  |  6   9  c14 |
:-----------------+----------+-------------:
|  7     1   8    | 6  2  4  |  9   5   3  |
|  3     4   6    | 5  7  9  |  1   2   8  |
|  2     5   9    | 1  3  8  |  7   4   6  |
:-----------------+----------+-------------:
|  4     8   23   | 9  1  7  |  23  6   5  |
|  59    7   35   | 8  6  2  |  34  1   49 |
|  19    6   12   | 3  4  5  |  8   7   29 |
'-----------------'----------'-------------'

(1)b1p16 =BUG+3= (54)r2c17 - (4=1)r3c9 => -1 r3c3; stte

[SpAce]

3r8c7=r8c3-(3=2)r7c3-(2=1)r9c3-r3c3=1r3c9=>3r8c7=1r3c9=>or +3r8c7=>stte; or+1r3c9=>stte;or (+3r8c7 and +1r3c9)=>stte.

Looks like circular reasoning to me. The chain doesn't prove anything except that either 3r8c7 or 1r3c9 must be true. It's a derived strong link, nothing else by itself. It makes no difference if you state that they both yield stte. A manual solver could not know that fact without trying them both all the way to the end. That's simply guessing. Sorry to say, but that's not even close to a valid resolution by any standards.

[Ajò Dimonios]

Space wrote:
Ajò Dimonios wrote:
3r8c7=r8c3-(3=2)r7c3-(2=1)r9c3-r3c3=1r3c9=>3r8c7=1r3c9=>or +3r8c7=>stte; or+1r3c9=>stte;or (+3r8c7 and +1r3c9)=>stte.

Looks like circular reasoning to me. The chain doesn't prove anything except that either 3r8c7 or 1r3c9 must be true. It's a derived strong link, nothing else by itself. It makes no difference if you state that they both yield stte. A manual solver could not know that fact without trying them both all the way to the end. That's simply guessing. Sorry to say, but that's not even close to a valid resolution by any standards.

No, I do not agree. The resolution is fully valid and also demonstrates the uniqueness of the solution.
3r8c7 = r8c3- (3 = 2) r7c3- (2 = 1) r9c3-r3c3 = 1r3c9 => 3r8c7 = 1r3c9 shows that there is a strong inference between two hypotheses r8c7 = 3 and r3c9 = 1. So at least one of the two hypotheses is valid. So if r8c7 = 3 is false then r3c9 = 1 is true. If r3c9 = 1 is true, through the insertion of singles it implies that r8c7 = 3 is true,so r8c7 = 3 is true. The insertion of r8c7 = 3 leads directly to the solution (stte). The same proof can be performed starting from the hypothesis that r3c9 = 1 is false. In this strong inference 3r8c7 = 1r3c9 both hypotheses are true.

Paolo

[SpAce]

No, I do not agree.

Of course That response was inevitable, which is why I didn't actually write it for you. It was meant to inform other people who might be wondering what the heck it was. I just gave them the facts. Of course it's up to them to decide whom they want to believe. For anyone with the tiniest amount of judgment it will be obvious. Anyone else, who cares.

The resolution is fully valid and also demonstrates the uniqueness of the solution.

Believe whatever you want. For obvious reasons I'm not going to debate anything with you. I can't think of a more futile effort. Both of us have now presented our sides, so there's no need to discuss this any further anyway. I'm pretty sure there's enough information on the table for most people to see the light.

PS. This issue has come up before, here and here at least. The first time I saw an attempt to use such an approach I actually thought it was really clever -- until I realized that it had serious problems. So, I understand that it might seem like a valid solution. But it isn't. Or at least all of us who participated in the discussion (SteveC, myself, Cenoman) agreed so, as far as I remember.

PPS. This is perhaps a little bit related, except that it's a valid resolution.

[Ajò Dimonios]

Space wrote:
Ajò Dimonios wrote:
No, I do not agree.

Of course That response was inevitable, which is why I didn't actually write it for you. It was meant to inform other people who might be wondering what the heck it was. I just gave them the facts. Of course it's up to them to decide whom they want to believe. For anyone with the tiniest amount of judgment it will be obvious. Anyone else, who cares.

The resolution is fully valid and also demonstrates the uniqueness of the solution.

Believe whatever you want. For obvious reasons I'm not going to debate anything with you. I can't think of a more futile effort. Both of us have now presented our sides, so there's no need to discuss this any further anyway. I'm pretty sure there's enough information on the table for most people to see the light.

PS. This issue has come up before, here and here at least. The first time I saw an attempt to use such an approach I actually thought it was really clever -- until I realized that it had serious problems. So, I understand that it might seem like a valid solution. But it isn't. Or at least all of us who participated in the discussion (SteveC, myself, Cenoman) agreed so, as far as I remember.

PPS. This is perhaps a little bit related, except that it's a valid resolution.

I'm sorry you don't admit your mistake. You probably have no valid arguments to refute what I wrote.

Paolo

[SpAce]

I'm sorry you don't admit your mistake. You probably have no valid arguments to refute what I wrote.

Indeed, just like last time I didn't This is exactly why I don't debate anything with you. Thank you for demonstrating my point, once again.

[eleven]

Unfortunately the elimination is not stte (or even btte).

oops, thanks. This should repair it:
249r189c9 = 16r1c69 - (1|6=58)r1c15 - (5|8=964)r8c159 => -9r8c7, -4r23c9

[SteveG48]

Paolo, I'm sorry but you're wrong. Your chain demonstrates that either 3r8c7 or 1r3c9, and possibly both, must be true. Unfortunately, it doesn't tell which of those things apply. Unless a solution tells someone "if you assign this or eliminate that then you are guaranteed to be correct and have singles to the end", then it's not a solution.

As it turns out in this puzzle, both 3r8c7 and 1r3c9 are true, but suppose that wasn't the case. Suppose 3r8c7 was false and 1r3c9 was true. How does your chain tell the solver which to assign and which to eliminate?

Now, if you can come up with a second chain that tells you that if 3r8c7 is true then 1r3c9 must also be true, then the two chains together give you the solution that you want.

[Ajò Dimonios]

SteveG48 wrote:
Your chain demonstrates that either 3r8c7 or 1r3c9, and possibly both, must be true.

I agree.

Unfortunately, it doesn't tell which of those things apply. Unless a solution tells someone "if you assign this or eliminate that then you are guaranteed to be correct and have singles to the end", then it's not a solution.

No, I don't need to use 3r8c7 or 1r3c9 backdoors.

As it turns out in this puzzle, both 3r8c7 and 1r3c9 are true, but suppose that wasn't the case. Suppose 3r8c7 was false and 1r3c9 was true. How does your chain tell the solver which to assign and which to eliminate?

Quite simply the net or chain of singles that is formed when 1r3c9 is true, which shows that r8c7 = 3 is true (I don't use the fact that 3r8c7 is a backdoor but only that, r8c7 = 3 is one of the singles) provides me this information . r8c7 = 3 true, contradicts the initial hypothesis that r8c7 = 3 is false (I don't need to get to the solution). If the initial hypothesis r8c7 ≠ 3 leads to prove that the opposite is true, it is mathematically that r8c7 = 3 is true.

Now, if you can come up with a second chain that tells you that if 3r8c7 is true then 1r3c9 must also be true, then the two chains together give you the solution that you want.

The second chain is simply the one that is present in each resolution r8c7 = 3 => Stte (contains the information that r3c9 = 1). At this point the fact that 1r3c9 is also a backdoor is not relevant

Paolo

[SteveG48]

As it turns out in this puzzle, both 3r8c7 and 1r3c9 are true, but suppose that wasn't the case. Suppose 3r8c7 was false and 1r3c9 was true. How does your chain tell the solver which to assign and which to eliminate?

Quite simply the net or chain of singles that is formed when 1r3c9 is true, which shows that r8c7 = 3 is true

Then write that chain. Combined with the previous chain you then have the argument "One of these two things is true (chain 1), and if one of them is true then the other is true (chain 2). Therefore both are true and can be assigned. QED"