Need help with a "diabolical" puzzle!

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Postby QBasicMac » Fri Jan 06, 2006 3:07 am

tso wrote:All valid Sudokus -- as well as any other similar logic puzzles -- are solvable by logic alone.


In my opinion, just as it an unfortunate misnomer to classify puzzles as invalid that have a single solution, so it is an unfortunate mistake to exclude T&E from logic. It is definately a logical solution.

The theorem you state should be worded "All valid Sudokus are solvable without recourse to the simpler and often more elegant T&E method" And you might even add "We look down on people who have no ability to detect these difficult and archane solutions and instead lazily use the straightforward and easy path to solution."

All fine. I accept that. But I cannot accept that T&E is not logical.

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Postby angusj » Fri Jan 06, 2006 7:10 am

QBasicMac wrote:All fine. I accept that. But I cannot accept that T&E is not logical.

While it's correct that systematically trying one possibility after another is logical, it's far from satisfying for the vast majority of puzzle solving enthusiasts.
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Postby tarek » Fri Jan 06, 2006 10:48 am

tso wrote:This does not appear to be a valid Nisio exclusion. If r7c8=7, there are 6 ways to place all the rest of the 7s


Interesting. Now I may have programmed it the wrong way, but if r7c8=7 then single elimination only from then will lead to a contradiction. which allows us to eliminate 7 from r7c8 leaving 2 as the only valid candidate.
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Postby tarek » Fri Jan 06, 2006 11:13 am

I've checked the Nishio definition here. Although my assumption and conclusion were correct, They don't fit the Nishio definition. They resemble a simple Guessing technique (compared to a Deep T&E). So ........ back to the drawing board
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Postby rubylips » Fri Jan 06, 2006 2:01 pm

Just to clarify, I believe r2c5:=8 is the only permissible Nishio elimination from the initial position. It doesn't help much.

Code: Select all
   247       5   28 |  479   4789    1 |    6    379  3789
     3    1478    6 |  479  45789    2 |  578   1579  5789
    17     178    9 |    3   5678  678 |    2    157     4
--------------------+------------------+------------------
    79     679    4 |    5      3  679 |    1      8     2
  1279  123679   23 |    8    679    4 |   57  35679  3579
     8    3679    5 |    1      2  679 |    4   3679   379
--------------------+------------------+------------------
     6    2489    1 |  479   4789    5 |    3     27    78
   245    2348  238 |    6    478  378 |    9    257     1
    59     389    7 |    2      1  389 |   58      4     6

  .  .  ? |  .  ?  . |  .  .  ?
  .  ?  . |  .  ?  . |  ?  .  ?
  .  ?  . |  .  ?  ? |  .  .  .
----------+----------+---------
  .  .  . |  .  .  . |  .  8  .
  .  .  . |  8  .  . |  .  .  .
  8  .  . |  .  .  . |  .  .  .
----------+----------+---------
  .  ?  . |  .  ?  . |  .  .  ?
  .  ?  ? |  .  ?  ? |  .  .  .
  .  ?  . |  .  .  ? |  ?  .  .
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Postby tso » Fri Jan 06, 2006 4:33 pm

tarek wrote:I've checked the Nishio definition here. Although my assumption and conclusion were correct, They don't fit the Nishio definition. They resemble a simple Guessing technique (compared to a Deep T&E). So ........ back to the drawing board


I think that definition is a little too strict -- I'm not completely sure that both of the Nishios I suggested measure up. The important thing about Nishio is that it can be accomplished mentally. It's a pen and paper tactic.



rubylips wrote:Just to clarify, I believe r2c5:=8 is the only permissible Nishio elimination from the initial position. It doesn't help much.


Right. The Nishio in 7s doesn't appear until after the xy-wing.


QBasicMac wrote:
tso wrote:All valid Sudokus -- as well as any other similar logic puzzles -- are solvable by logic alone.


In my opinion, just as it an unfortunate misnomer to classify puzzles as invalid that have a single solution, so it is an unfortunate mistake to exclude T&E from logic. It is definately a logical solution.



You are correct. It wasn't my intention to sully T&E -- often when novices ask this question they're using T&E as a synonym for guessing -- but of course you are right. Backtracking only differs by degree from other logical tactics.

I'm personally looking for the methods that are subjectively the most fun to use -- finishing off the puzzle is rarely the point -- the point is to trick myself into thinking that I'm *clever*. Trial and error doesn't do that for me.

QBasicMac wrote:"We look down on people who have no ability to detect these difficult and archane solutions and instead lazily use the straightforward and easy path to solution."


I hadn't noticed anyone condescending to *solvers* using trial and error, but when someone asks here for a nudge or a "next logical step", suggesting T&E is simply *not* the answer they're looking for, anymore than "put a 5 in the center cell". And, when someone asks if all sudokus can be solved "by logic alone without resorting to trial and error", though the question is flawed, we *know* what they are really asking. They want to know if they all can -- in layman's terms -- be solved without guessing. They *already know* they can be solved by by trial and error.
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Postby QBasicMac » Fri Jan 06, 2006 7:48 pm

tso wrote:I'm personally looking for the methods that are subjectively the most fun to use -- finishing off the puzzle is rarely the point -- the point is to trick myself into thinking that I'm *clever*. Trial and error doesn't do that for me.


That is a good way to look at it. Especially "subjectively" and "rarely the point".

I guess I got off track when I saw T&E (a technique I subjectively like) classified as not logical. Sorry for the disturbance.

By the way, even I would say that blind T&E whereby the solver immediately guesses numbers in all cells, using only the rule that the number must not already be in the row/column/box would not yield much pleasure.

I like this: Use easy techniques up to and including quads, X-Tree and Swordfish and very simple coloring (one candidate value alternating). Get stuck, use T&E not to solve the puzzle but to eliminate a candidate. Hopefully a clever guess (that is satisfying!) will lead to such elimination. Then continue with easy techniques as before.

But as you said, "subjective". While I might really be disgusted with techniques based on the theory the puzzle has a unique solution, I have to imagine others greatly enjoying that.

My job: Ignore posts that bog down in what I feel are Boring Arcane Techniques without wasting forum space by voicing my disapproval which naturally nobody wants to hear. If I feel a newbie actually wants to find a solution and I feel BAT is beyond his reach, I should, without going off the deep end, simply provide my T&E hint.

Again, thanks, TSO, for the clarification and I won't bother you again about T&E (New Year's resolution #1)
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Postby BL » Fri Jan 06, 2006 10:50 pm

4 5 2 | 9 8 1 | 6 3 7
3 7 6 | 4 5 2 | 8 1 9
1 8 9 | 3 7 6 | 2 5 4
----------------------
7 6 4 | 5 3 9 | 1 8 2
2 1 3 | 8 6 4 | 7 9 5
8 9 5 | 1 2 7 | 4 6 3
-----------------------
6 4 1 | 7 9 5 | 3 2 8
5 2 8 | 6 4 3 | 9 7 1
9 3 7 | 2 1 8 | 5 4 6
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Postby tarek » Sat Jan 07, 2006 3:20 am

I think i've got it finally:
Code: Select all
*--------------------------------------------------------------------------*
| 247     5       28     | 479     4789    1      | 6       379     3789   |
| 3       1478    6      | 479     45789   2      | 578     1579    5789   |
| 17      178     9      | 3       5678    678    | 2       157     4      |
|------------------------+------------------------+------------------------|
| 79      679     4      | 5       3       679    | 1       8       2      |
| 1279    123679  23     | 8       679     4      | 57      35679   3579   |
| 8       3679    5      | 1       2       679    | 4       3679    379    |
|------------------------+------------------------+------------------------|
| 6       2489    1      | 479     4789    5      | 3       27      78     |
| 245     2348    238    | 6       478     378    | 9       257     1      |
| 59      389     7      | 2       1       389    | 58      4       6      |
*--------------------------------------------------------------------------*
Eliminating 7 From r5c9 (XY wing)
Eliminating 7 From r6c9 (XY wing)
*--------------------------------------------------------------------------*
| 247     5       28     | 479     4789    1      | 6       379     3789   |
| 3       1478    6      | 479     45789   2      | 578     1579    5789   |
| 17      178     9      | 3       5678    678    | 2       157     4      |
|------------------------+------------------------+------------------------|
| 79      679     4      | 5       3       679    | 1       8       2      |
| 1279    123679  23     | 8       679     4      | 57      35679   359    |
| 8       3679    5      | 1       2       679    | 4       3679    39     |
|------------------------+------------------------+------------------------|
| 6       2489    1      | 479     4789    5      | 3       27      78     |
| 245     2348    238    | 6       478     378    | 9       257     1      |
| 59      389     7      | 2       1       389    | 58      4       6      |
*--------------------------------------------------------------------------*
7 in r7c8 would lead to a contradiction(Guess)
*--------------------------------------------------------------------------*
| 247     5       28     | 479     4789    1      | 6       379     3789   |
| 3       1478    6      | 479     45789   2      | 578     1579    5789   |
| 17      178     9      | 3       5678    678    | 2       157     4      |
|------------------------+------------------------+------------------------|
| 79      679     4      | 5       3       679    | 1       8       2      |
| 1279    123679  23     | 8       679     4      | 57      35679   359    |
| 8       3679    5      | 1       2       679    | 4       3679    39     |
|------------------------+------------------------+------------------------|
| 6       489     1      | 479     4789    5      | 3       2       78     |
| 245     2348    238    | 6       478     378    | 9       57      1      |
| 59      389     7      | 2       1       389    | 58      4       6      |
*--------------------------------------------------------------------------*
Any Candidate in r3c8 forces r1c3 to have only 2 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r3c2 to have only 8 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r3c6 to have only 6 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r5c3 to have only 3 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r8c3 to have only 8 as valid Candidates (Forcing Chains)

There was no Nishio in the steps above if xy wing was used
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Postby QBasicMac » Sat Jan 07, 2006 5:16 am

Hi, Tarek. Hope you don't mind my reposting your results so they fit on my cheaper monitor.

:DMac
Code: Select all
*-----------------------------------------------*
| 247      5  28 |479  4789   1 |  6   379 3789 |
|   3   1478   6 |479 45789   2 |578  1579 5789 |
|  17    178   9 |  3  5678 678 |  2   157    4 |
|----------------+--------------+---------------|
|  79    679   4 |  5     3 679 |  1     8    2 |
|1279 123679  23 |  8   679   4 | 57 35679 3579 |
|   8   3679   5 |  1     2 679 |  4  3679  379 |
|----------------+--------------+---------------|
|   6   2489   1 |479  4789   5 |  3    27   78 |
| 245   2348 238 |  6   478 378 |  9   257    1 |
|  59    389   7 |  2     1 389 | 58     4    6 |
*-----------------------------------------------*
Eliminating 7 From r5c9 (XY wing)
Eliminating 7 From r6c9 (XY wing)
*-----------------------------------------------*
| 247      5  28 |479  4789   1 |  6   379 3789 |
|   3   1478   6 |479 45789   2 |578  1579 5789 |
|  17    178   9 |  3  5678 678 |  2   157    4 |
|----------------+--------------+---------------|
|  79    679   4 |  5     3 679 |  1     8    2 |
|1279 123679  23 |  8   679   4 | 57 35679  359 |
|   8   3679   5 |  1     2 679 |  4  3679   39 |
|----------------+--------------+---------------|
|   6   2489   1 |479  4789   5 |  3    27   78 |
| 245   2348 238 |  6   478 378 |  9   257    1 |
|  59    389   7 |  2     1 389 | 58     4    6 |
*-----------------------------------------------*
7 in r7c8 would lead to a contradiction(Guess)
*-----------------------------------------------*
| 247      5  28 |479  4789   1 |  6   379 3789 |
|   3   1478   6 |479 45789   2 |578  1579 5789 |
|  17    178   9 |  3  5678 678 |  2   157    4 |
|----------------+--------------+---------------|
|  79    679   4 |  5     3 679 |  1     8    2 |
|1279 123679  23 |  8   679   4 | 57 35679  359 |
|   8   3679   5 |  1     2 679 |  4  3679   39 |
|----------------+--------------+---------------|
|   6    489   1 |479  4789   5 |  3     2   78 |
| 245   2348 238 |  6   478 378 |  9    57    1 |
|  59    389   7 |  2     1 389 | 58     4    6 |
*-----------------------------------------------*
Any Candidate in r3c8 forces r1c3 to have only 2 as valid Candidates  (Forcing Chains)
Any Candidate in r3c8 forces r3c2 to have only 8 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r3c6 to have only 6 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r5c3 to have only 3 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r8c3 to have only 8 as valid Candidates (Forcing Chains)
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Posts: 441
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Postby tso » Sat Jan 07, 2006 5:56 am

tarek wrote:I think i've got it finally:
Code: Select all
*-----------------------------------------------*
| 247      5  28 |479  4789   1 |  6   379 3789 |
|   3   1478   6 |479 45789   2 |578  1579 5789 |
|  17    178   9 |  3  5678 678 |  2   157    4 |
|----------------+--------------+---------------|
|  79    679   4 |  5     3 679 |  1     8    2 |
|1279 123679  23 |  8   679   4 | 57 35679  359 |
|   8   3679   5 |  1     2 679 |  4  3679   39 |
|----------------+--------------+---------------|
|   6    489   1 |479  4789   5 |  3     2   78 |
| 245   2348 238 |  6   478 378 |  9    57    1 |
|  59    389   7 |  2     1 389 | 58     4    6 |
*-----------------------------------------------*

Any Candidate in r3c8 forces r1c3 to have only 2 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r3c2 to have only 8 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r3c6 to have only 6 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r5c3 to have only 3 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r8c3 to have only 8 as valid Candidates (Forcing Chains)


You do not *seem* to be using forcing chains in the way they are commonly known. Each link must be implied by the previous link and in turn imply the next -- "if A then B, if B then C, if C then D, etc. You seem to have -- "if A then by whatever means possible, eventually B." The deduction is valid, but they are not forcing chains. For example, r3c2 has three candidates -- how does r3c8=5 lead to r3c2=8, when the candidate 8 in r3c2 is not a conjugate in its row, column or box? Both the 1 and 7 must be eliminated -- no previous single link can do this.
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Postby tarek » Sat Jan 07, 2006 11:56 am

tso wrote:You do not *seem* to be using forcing chains in the way they are commonly known


You are Probably right. However, I do think it is a forcing chain. It basically follows the deduction That AB is always the end result.

assuming cell 1 is abc
assuming cell 2 is ABC

if cell1=a then cell2=AB
if cell1=b then cell2=AB
if cell1=c then cell2=AB
if that is the case , then you can safely assume that cell 2 must be AB.

in any case, I also made a mistake in programming the Nishio concept, after The XY reduction there are 2 possible Nishio eliminations (You mentioned that), but then I need to guess & finally, solve it via MY forcing chains
Code: Select all
*--------------------------------------------------------------------------*
| 247     5       28     | 479     4789    1      | 6       379     3789   |
| 3       1478    6      | 479     45789   2      | 578     1579    5789   |
| 17      178     9      | 3       5678    678    | 2       157     4      |
|------------------------+------------------------+------------------------|
| 79      679     4      | 5       3       679    | 1       8       2      |
| 1279    123679  23     | 8       679     4      | 57      35679   3579   |
| 8       3679    5      | 1       2       679    | 4       3679    379    |
|------------------------+------------------------+------------------------|
| 6       2489    1      | 479     4789    5      | 3       27      78     |
| 245     2348    238    | 6       478     378    | 9       257     1      |
| 59      389     7      | 2       1       389    | 58      4       6      |
*--------------------------------------------------------------------------*
Eliminating 7 From r5c9 (XY wing)
Eliminating 7 From r6c9 (XY wing)
*--------------------------------------------------------------------------*
| 247     5       28     | 479     4789    1      | 6       379     3789   |
| 3       1478    6      | 479     45789   2      | 578     1579    5789   |
| 17      178     9      | 3       5678    678    | 2       157     4      |
|------------------------+------------------------+------------------------|
| 79      679     4      | 5       3       679    | 1       8       2      |
| 1279    123679  23     | 8       679     4      | 57      35679   359    |
| 8       3679    5      | 1       2       679    | 4       3679    39     |
|------------------------+------------------------+------------------------|
| 6       2489    1      | 479     4789    5      | 3       27      78     |
| 245     2348    238    | 6       478     378    | 9       257     1      |
| 59      389     7      | 2       1       389    | 58      4       6      |
*--------------------------------------------------------------------------*
7 in r3c6 would make placing other 7s impossible (Nishio)
*--------------------------------------------------------------------------*
| 247     5       28     | 479     4789    1      | 6       379     3789   |
| 3       1478    6      | 479     45789   2      | 578     1579    5789   |
| 17      178     9      | 3       5678    68     | 2       157     4      |
|------------------------+------------------------+------------------------|
| 79      679     4      | 5       3       679    | 1       8       2      |
| 1279    123679  23     | 8       679     4      | 57      35679   359    |
| 8       3679    5      | 1       2       679    | 4       3679    39     |
|------------------------+------------------------+------------------------|
| 6       2489    1      | 479     4789    5      | 3       27      78     |
| 245     2348    238    | 6       478     378    | 9       257     1      |
| 59      389     7      | 2       1       389    | 58      4       6      |
*--------------------------------------------------------------------------*
8 in r2c5 would make placing other 8s impossible (Nishio)
*--------------------------------------------------------------------------*
| 247     5       28     | 479     4789    1      | 6       379     3789   |
| 3       1478    6      | 479     4579    2      | 578     1579    5789   |
| 17      178     9      | 3       5678    68     | 2       157     4      |
|------------------------+------------------------+------------------------|
| 79      679     4      | 5       3       679    | 1       8       2      |
| 1279    123679  23     | 8       679     4      | 57      35679   359    |
| 8       3679    5      | 1       2       679    | 4       3679    39     |
|------------------------+------------------------+------------------------|
| 6       2489    1      | 479     4789    5      | 3       27      78     |
| 245     2348    238    | 6       478     378    | 9       257     1      |
| 59      389     7      | 2       1       389    | 58      4       6      |
*--------------------------------------------------------------------------*
7 in r7c8 would lead to a contradiction (Guess)
*--------------------------------------------------------------------------*
| 247     5       28     | 479     4789    1      | 6       379     3789   |
| 3       1478    6      | 479     4579    2      | 578     1579    5789   |
| 17      178     9      | 3       5678    68     | 2       157     4      |
|------------------------+------------------------+------------------------|
| 79      679     4      | 5       3       679    | 1       8       2      |
| 1279    123679  23     | 8       679     4      | 57      35679   359    |
| 8       3679    5      | 1       2       679    | 4       3679    39     |
|------------------------+------------------------+------------------------|
| 6       489     1      | 479     4789    5      | 3       2       78     |
| 245     2348    238    | 6       478     378    | 9       57      1      |
| 59      389     7      | 2       1       389    | 58      4       6      |
*--------------------------------------------------------------------------*
Any Candidate in r3c8 forces r1c3 to have only 2 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r3c2 to have only 8 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r3c6 to have only 6 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r5c3 to have only 3 as valid Candidates (Forcing Chains)
Any Candidate in r3c8 forces r8c3 to have only 8 as valid Candidates (Forcing Chains)
Last edited by tarek on Sat Jan 07, 2006 8:46 am, edited 2 times in total.
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Postby tarek » Sat Jan 07, 2006 11:58 am

QBasicMac wrote:Hi, Tarek. Hope you don't mind my reposting your results so they fit on my cheaper monitor


Thanx for that, I'll choose a smaller font next time.
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Postby bennys » Sat Jan 07, 2006 9:09 pm

here is what I found
Code: Select all
+----------------------+----------------------+----------------------+
| 247    5      28     | 479    4789   1      | 6      379    3789   |
| 3      1478   6      | 479    45789  2      | 578    1579   5789   |
|*17    *178    9      | 3      5678   678    | 2     *157    4      |
+----------------------+----------------------+----------------------+
| 79     679    4      | 5      3      679    | 1      8      2      |
| 1279   123679 23     | 8      679    4      | 57     35679  3579   |
| 8      3679   5      | 1      2      679    | 4      3679   379    |
+----------------------+----------------------+----------------------+
| 6      2489   1      | 479    4789   5      | 3      27     78     |
| 245    2348   238    | 6      478    378    | 9      257    1      |
| 59     389    7      | 2      1      389    | 58     4      6      |
+----------------------+----------------------+----------------------+

R3C2=8 => R8C3=8 => R9C6=8 (the only 8 left in C6)=>R9C7=5

R3C2<>8 =>R3C8=5 => R9C7=5

which mean that R9C7=5 and that solve the puzzle.
Last edited by bennys on Sat Jan 07, 2006 9:42 pm, edited 1 time in total.
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Postby tso » Sun Jan 08, 2006 1:10 am

tarek wrote:
tso wrote:You do not *seem* to be using forcing chains in the way they are commonly known


You are Probably right. However, I do think it is a forcing chain. It basically follows the deduction That AB is always the end result.


A "chain" is a series of links. Each link is attached to exactly two others. There are many other ways to connect links -- they are not chains.

A leads to B, B leads to C, therefore A leads to C -- is a chain. Each "link" is simply the fact that a particular state in one cell always forces a particular state in another. The whole point of forcing chains is that the individual links can be identified descretely and then strung together -- without solving the puzzle and backtracking. You haven't spelled out what your chains are or how you arrived at them, or how we could find them ourselves. Without other information, I'd have to guess that you entered each possible number into a cell, thus trifurcating the single puzzle into three descrete puzzles, solved them all from that point using simpler logic and looked for cells in all three that ended up with the same number. It's a forcing *net* or trial and error or backtracking or brute force or ... i dunno for sure ... but it isn't forcing chains.


tarek wrote:Any Candidate in r3c8 forces r3c2 to have only 8 as valid Candidates (Forcing Chains)

Can you spell out the chain that leads from r3c8=5 to r3c2=8?

tarek wrote:Any Candidate in r3c8 forces r3c6 to have only 6 as valid Candidates (Forcing Chains)

Can you spell out the chain that leads from r3c8=5 to r3c6=6?
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