Valid Nice Loop?

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Valid Nice Loop?

Postby Karlson » Tue May 30, 2006 4:20 pm

Here the Sudoku:
Code: Select all
 . . . | . . 7 | 2 5 .
 . 1 . | 5 8 . | . . 3
 5 . 4 | . . 9 | . . .
-------+-------+------
 . . 7 | . . 3 | 5 9 .
 3 . . | . 5 . | 1 . 7
 2 5 1 | 9 7 6 | . . .
-------+-------+------
 . . 6 | 3 . . | 8 . 5
 . . . | . . . | . 7 .
 1 . . | 7 . . | . . .


 689   3689  389   | 146   1346  7     | 2     5     14689
 679   1     29    | 5     8     24    | 4679  46    3   
 5     23678 4     | 126   1236  9     | 67    168   168 
-------------------+-------------------+-------------------
 468   468   7     | 1248  124   3     | 5     9     26   
 3     4689  89    | 248   5     248   | 1     26    7   
 2     5     1     | 9     7     6     | 34    348   48   
-------------------+-------------------+-------------------
 479   2479  6     | 3     249   124   | 8     124   5   
 489   23489 23589 | 2468  2469  12458 | 3469  7     12469
 1     23489 23589 | 7     2469  2458  | 3469  2346  2469

my nice loop - the solution is trivial after these exclusions:
[R2C3]-9-[R2C7]=9=[R1C9]-6-[R4C9]=6=[R5C8]=6=[R5C2]=9=[R5C3]-9-[R2C3] => [R2C3]<>9 [R1C9]<>6

Regards,
Karlson
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Re: Valid Nice Loop?

Postby ronk » Tue May 30, 2006 4:51 pm

Karlson wrote:my nice loop - the solution is trivial after these exclusions:
[R2C3]-9-[R2C7]=9=[R1C9]-6-[R4C9]=6=[R5C8]=6=[R5C2]=9=[R5C3]-9-[R2C3] => [R2C3]<>9 [R1C9]<>6

The translation, with "->" standing for "implies", of the highlighted portion is:

r2c3=9 -> r2c7<>9 -> r1c9=9 -> r1c9=6

r1c9 can't be two different values ... so I stopped checking there. I'm unable to find a valid nice loop for that same exclusion.
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Postby Sped » Tue May 30, 2006 5:13 pm

[R2C3]-9-[R2C7]=9=[R1C9]-6-[R4C9]=6=[R5C8]=6=[R5C2]=9=[R5C3]-9-[R2C3] => [R2C3]<>9 [R1C9]<>6


A simple discontinuous nice loop follows the rules except at one cell, the disontinuity.

Your loop violates the rules at three cells:

-9-[R2C3]-9- Weak link to weak link must be done on different candidates.
=9=[R1C9]-6- Strong link to weak link must be done on the same candidate.
=6=[R5C8]=6= Strong link to strong link must be done on different candidates.
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Postby Karlson » Tue May 30, 2006 5:48 pm

Thanks for clearing it up:)
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Postby Karlson » Wed May 31, 2006 7:33 pm

This one should be correct:
[R7C9]-6-[R4C9]-7-[R6C7]-9-[R6C5]-6-[R6C1]=6=[R7C1]-6-[R7C9] => [R7C9]<>6
Code: Select all
 4     9     1     | 6     5     7     | 8     2     3   
 35    35    6     | 4     2     8     | 1     7     9   
 8     2     7     | 9     1     3     | 6     4     5   
-------------------+-------------------+-------------------
 9     45    8     | 2     37    1     | 3457  356   67   
 2     67    345   | 37    69    45    | 459   8     1   
 67    1     345   | 8     69    45    | 79    35    2   
-------------------+-------------------+-------------------
 356   34567 45    | 1     8     2     | 357   9     67   
 37    8     9     | 5     37    6     | 2     1     4   
 1     3567  2     | 37    4     9     | 357   356   8   
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Postby Sped » Wed May 31, 2006 8:18 pm

[R7C9]-6-[R4C9]-7-[R6C7]-9-[R6C5]-6-[R6C1]=6=[R7C1]-6-[R7C9] => [R7C9]<>6

Your loop is correct.

It doesn't solve the puzzle, but it does move you along.

After your loop there were 2 or 3 xy chains, and a BUG+1 finish.

Nice puzzle. What was the starting grid?
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Postby Karlson » Wed May 31, 2006 8:21 pm

I'm sorry - already deleted the sudoku ...:(
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Postby Myth Jellies » Thu Jun 01, 2006 2:24 am

Some AIC's (very similar to nice loops) for the original puzzle...
Code: Select all
 *--------------------------------------------------------------------*
 | 689    3689   389    | 146    1346   7      | 2      5      14689  |
 |N679    1     A29     | 5      8     G24     |M4679 MF46     3      |
 | 5     Q23678  4      | 126    1236   9      |L67    H168   H168    |
 |----------------------+----------------------+----------------------|
 |C468   C468    7      |K1248' K1'24   3      | 5      9     D26     |
 | 3      4689  B89     |J248    5     J248    | 1     E26     7      |
 | 2      5      1      | 9      7      6      | 34     348    48     |
 |----------------------+----------------------+----------------------|
 |O479   P2479   6      | 3      249    124    | 8      124    5      |
 | 489    23489  23589  | 2468   2469   12458  | 3469   7      12469  |
 | 1      23489  23589  | 7      2469   2458   | 3469   2346   2469   |
 *--------------------------------------------------------------------*

    E2 = E6 - F6 = F4 - G4 = G2; => r5c6 <> 2
    A2 = A9 - B9 = B8 - C8 = C(4&6) - D6 = E6 - F6 = F4 - G4 = G2 (- A2); closed loop => r189c3 <> 9, r5c2 <> 8, r39c8 <> 6, and r2c7 <> 4
    H1 = H(6&8) - F6 = F4 - G4 = G2 - A2 = A9 - B9 = B8 - J8 = J(2&4) - K(24) = K(1'&8'); => r3c5 <> 1
    L7 = L6 - M6 = N6 - N7 = O7 - P7 = Q7 (- L7); closed loop => r1c9 & r3c89 <> 6, and r2c1 <> 9;

These don't crack it, but it gets things closer.
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Postby RW » Thu Jun 01, 2006 10:40 am

Lots of people are asking if their loops, coloring grids etc are correct. A basic rule that applies to ALL non-uniqueness related reductions:

Code: Select all
If a pattern 'P' let's you eliminate 'a' from cell Y, then assigning the value 'a' to cell Y would lead to a contradiction within the pattern 'P'.


This is true for anything from singles to complex error nets. Looking at your first nice loop, I was able to assign a 9 in r2c3 and then fill all the mentioned cells without causing an immediate contradiction => The elimination was false. Same goes for the r1c9<>6. Looking at your second loop, if I assigned 6 to r7c9 and then tried to fill the other mentioned cells, then I reach a contradiction (no 6 in column 1), the elimination is correct. This way anybody should be able to check if their complex eliminations are valid.

Another important rule: Never make an elimination because it reminds you of something you read somewhere! Only make eliminations if you understand the contradiction the eliminated value would cause.

And a BUG-lite solution to the second puzzle (after the nice loop):

Code: Select all
 *-----------------------------------------------------------*
 | 4     9     1     | 6     5     7     | 8     2     3     |
 |*35   *35    6     | 4     2     8     | 1     7     9     |
 | 8     2     7     | 9     1     3     | 6     4     5     |
 |-------------------+-------------------+-------------------|
 | 9     45    8     | 2     37    1     | 47    35    6     |
 | 2     67    345   | 37    69    45    | 49    8     1     |
 | 67    1     345   | 8     69    45    | 79    35    2     |
 |-------------------+-------------------+-------------------|
 |*35+6  3456  45    | 1     8     2     |*35    9     7     |
 | 37    8     9     | 5     37    6     | 2     1     4     |
 | 1    *35+7  2     | 37    4     9     |*35    6     8     |
 *-----------------------------------------------------------*


If r8c1=7 (=>r9c2<>7) => r6c1=6 (=r7c1<>6) => BUG-lite in r2c12, r7c17 and r9c27 => r8c1<>7

RW
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Another Solution for the Second Puzzle

Postby Carcul » Thu Jun 01, 2006 1:07 pm

Code: Select all
 *--------------------------------------------------*
 | 4     9      1   | 6   5     7  | 8      2    3  |
 | 35    35     6   | 4   2     8  | 1      7    9  |
 | 8     2      7   | 9   1     3  | 6      4    5  |
 |------------------+--------------+----------------|
 | 9     34567  8   | 2   367   1  | 3457   356  67 |
 | 2     34567  345 | 37  3679  45 | 34579  8    1  |
 | 3567  1      345 | 8   3679  45 | 34579  356  2  |
 |------------------+--------------+----------------|
 | 3567  34567  345 | 1   8     2  | 357    9    67 |
 | 37    8      9   | 5   37    6  | 2      1    4  |
 | 1     3567   2   | 37  4     9  | 357    356  8  |
 *--------------------------------------------------*


(The grid looks different from the one of Karlson, because of manual transcription of the clues to Simple Sudoku).

1. [r5c4](-3-[r4c59]-6,7-[r4c2])-3-[r9c4]=3=[r8c5]=7=[r8c1]-7-[r6c1]
=7=[r5c2]=6=[r5c5]-6-[r4c5]=6=[r4c9]-6-[r46c8]=6=[r9c8]-6-[r9c2]
=6=[r7c2]=4=[r7c3](-4-[r5c3])-4-[r6c38]-5-[r6c6]=5=[r5c6]-5-[r5c3]
-3-[r5c4], => r5c4<>3.

2. [r4c2]-7-[r4c9]=7=[r7c9]-7-[r7c1]=7=[r6c1]-7-[r4c2], => r4c2<>7
which solves the puzzle.

(Step 1, if properly adjusted, applied to the grid of Karlson solve it directly).

Carcul
Last edited by Carcul on Fri Jun 02, 2006 5:19 am, edited 5 times in total.
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Postby ronk » Thu Jun 01, 2006 1:53 pm

Myth Jellies wrote:
Code: Select all
 *-----------------------------------------------------------*
 | 689   3689  389   | 146   1346   7    | 2     5    14689  |
 |N679   1    A29    | 5     8     G24   |M4679 MF46   3     |
 | 5    Q23678 4     | 126   1236   9    |L67   H168  H168   |
 |-------------------+-------------------+-------------------|
 |C468  C468   7     |K1248' K1'24  3    | 5     9    D26    |
 | 3     4689 B89    |J248   5     J248  | 1    E26    7     |
 | 2     5     1     | 9     7      6    | 34    348   48    |
 |-------------------+-------------------+-------------------|
 |O479  P2479  6     | 3     249    124  | 8     124   5     |
 | 489   23489 23589 | 2468  2469  12458 | 3469  7     12469 |
 | 1     23489 23589 | 7     2469   2458 | 3469  2346  2469  |
 *-----------------------------------------------------------*

    E2 = E6 - F6 = F4 - G4 = G2; => r5c6 <> 2
    A2 = A9 - B9 = B8 - C8 = C(4&6) - D6 = E6 - F6 = F4 - G4 = G2 (- A2); closed loop => r189c3 <> 9, r5c2 <> 8, r39c8 <> 6, and r2c7 <> 4
    H1 = H(6&8) - F6 = F4 - G4 = G2 - A2 = A9 - B9 = B8 - J8 = J(2&4) - K(24) = K(1'&8'); => r3c5 <> 1
    L7 = L6 - M6 = N6 - N7 = O7 - P7 = Q7 (- L7); closed loop => r1c9 & r3c89 <> 6, and r2c1 <> 9;

For the 2nd, r5c2<>4 [edit: r4c4 and r4c5 are] also a valid exclusions.

For the 3rd, defining set J = {r4c5,r5c46} would simplify the expression a little.

In the 4th, I would've missed the r2c1<>9 exclusion. How do you think to even look for that?

[edit: added two missed exclusions]
Last edited by ronk on Sat Jun 03, 2006 7:30 am, edited 1 time in total.
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Postby r.e.s. » Thu Jun 01, 2006 11:51 pm

Carcul,

As soon as I opened this thread in my Firefox browser and began reading the first message, I knew you had posted somewhere further down:) -- because half the window was off to the right for every posting on the page (requiring scrolling to read anything that far over)! I've been noticing this in other posts of yours, and have been meaning to mention it:

Did you know that (at least for Firefox users) one single posting of yours with just one of those very long chains having no spaces in it, affects the display of all the other messages on the page?
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Postby Sped » Fri Jun 02, 2006 12:16 am

r.e.s. wrote:Carcul,

As soon as I opened this thread in my Firefox browser and began reading the first message, I knew you had posted somewhere further down:) -- because half the window was off to the right for every posting on the page (requiring scrolling to read anything that far over)! I've been noticing this in other posts of yours, and have been meaning to mention it:

Did you know that (at least for Firefox users) one single posting of yours with just one of those very long chains having no spaces in it, affects the display of all the other messages on the page?


Heh. So that's what's going on. It's Firefox's problem. When I look at this thread in IE I don't have to scroll right or left, but with Firefox I do.

A space every now and then might help readability in both browsers. But really.. it's Firefox's problem, not Carcul's.
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Postby r.e.s. » Fri Jun 02, 2006 1:50 am

Sped wrote:But really.. it's Firefox's problem, not Carcul's.

It's Carcul's problem if he wants to encourage Firefox users to read his messages.:)
(I meant the message as informational only, in case Carcul was unaware of the situation.)
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Postby ravel » Fri Jun 02, 2006 8:16 am

[Edit: deleted the test string]
Last edited by ravel on Fri Jun 02, 2006 5:52 am, edited 1 time in total.
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