Colouring (?) ~solved - thanks~

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Colouring (?) ~solved - thanks~

Postby barbe rouge » Thu Jan 26, 2006 2:29 pm

Hallo all,
could you please explain to me what kind
of colouring is the one below? Shouldn't
there be some kind of connection between
c4r5 and c7r3, or am I losing something?
Thank you:D

Image

Code: Select all
---------------------------------------------------------
| 456   368   3468  | 9     1    7  | 2      58    346  |
| 456   1     4689  | 3     46   2  | 578    578   469  |
| 2     369   7     | 8     5    46 | 36     1     3469 |
| ------------------+---------------+-------------------|
| 8     69    169   | 7     46   5  | 146    3     2    |
| 3     2     5     | 1     9    46 | 467    67    8    |
| 7     4     16    | 2     3    8  | 16     9     5    |
| ------------------+---------------+-------------------|
| 1     5     46    | 46    8    3  | 9      2     7    |
| 9     7     38    | 56    2    1  | 3568   4     36   |
| 46    38    2     | 456   7    9  | 358    568   1    |
---------------------------------------------------------
Last edited by barbe rouge on Sat Jan 28, 2006 5:03 pm, edited 2 times in total.
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Postby CathyW » Thu Jan 26, 2006 4:45 pm

Sorry - impossible to see your candidates in the grid at that size. Can you post the original puzzle, and where you've got to and hopefully someone can help with the next step.

You can't deduce anything from colouring just three squares. Check out AngusJ's definition's here: http://angusj.com/sudoku/hints.php - scroll down to the section titled Solving with Colours or from Sadman Sudoku: http://www.simes.clara.co.uk/programs/sudokutechnique12.htm
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Postby barbe rouge » Thu Jan 26, 2006 5:23 pm

CathyW,
thank you very much for the reply.:D
If you click on the photo, it doesn't open in a bigger image,
or the bigger image is still too small?

I have seen both angusj, and sadmans instructions,
but as you say I also thought that you cannot deduct
colouring from these squares.

Also the Simple Sudoku that I use, does not gine any
hint on this position, which I find it a little perplexing,
if it is colouring, since it uses colours.

Sudo Cue however, this is what it gives as a hint:
coloring value 6 found a connected pair and
highlights these three squares.
The problem is this
Last edited by barbe rouge on Fri Jan 27, 2006 7:32 am, edited 1 time in total.
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Postby CathyW » Thu Jan 26, 2006 8:41 pm

Hi Barbe

Didn't realise a bigger image would open up if I clicked on it!! Sorry.

Your puzzle is at this point:
Code: Select all
 
{456}  {368}  {3468} {9}    {1}    {7}    {2}    {58}   {346} 
{456}  {1}    {4689} {3}    {46D}  {2}    {578}  {578}  {469} 
{2}    {369}  {7}    {8}    {5}    {46D}  {36}   {1}    {3469}
{8}    {69}   {16*9} {7}    {46C}  {5}    {146}  {3}    {2}   
{3}    {2}    {5}    {1}    {9}    {46C}  {467}  {67}   {8}   
{7}    {4}    {16}   {2}    {3}    {8}    {16}   {9}    {5}   
{1}    {5}    {46A}  {46B}  {8}    {3}    {9}    {2}    {7}   
{9}    {7}    {38}   {56}   {2}    {1}    {3568} {4}    {36}   
{46B}  {38}   {2}    {456}  {7}    {9}    {3568} {568}  {1}   


Interestingly Simple Sudoku has no hint to offer at this stage. I think multi-colouring on 6s can offer the same elimination, but the {4,6} pairs must be significant in the Sudocue solver. At the intersection of squares marked A and C i.e. r4c3, you can eliminate 6.

Needs someone who knows about 'linked pairs' to check this out, but I couldn't find a chain that would get the same result.

Anyway, having eliminated that 6 in r4c3, you can use xy-wing (r4c2,3; r6c7) to eliminate another 6 in r4c7.

Then try multi-colouring on 5s for some eliminations.
Another xy-wing, a few single 3s, another xy-wing and the rest should be singles.

Hope that helps, but I'd still like someone else's opinion on that first elimination of 6.

This was a tough puzzle indeed - where did it come from?
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Postby Carcul » Thu Jan 26, 2006 8:49 pm

Hi Barbe Rouge and CathyW.

CathyW wrote:Needs someone who knows about 'linked pairs' to check this out, but I couldn't find a chain that would get the same result.


I also do not know what SudoCue means with "linked pairs", but here is a chain that proves r4c3 cannot be "6":

[r4c3]=1=[r4c7]-1-[r6c7]-6-[r5c8]=6=[r9c8]-6-[r9c1]=6=[r7c3]-6-[r4c3] => r4c3<>6.

However, this chain does not solve the puzzle. A faster solution can be reached from the grid posted above by Barbe Rouge if we note that we have an Almost Unique Rectangle in cells r4c3/r4c7/r6c3/r6c7 with the link [r4c3]=9|4=[r4c7], and we can deduce

[r3c2]=9=[r4c2]-9-[r4c3]=9|4=[r4c7]-4-[r4c5]=4=[r2c5]-4-[r3c6](-6-[r3c2])-6-[r3c7]-3-[r3c2]

which implies r3c2<>3,6 => r3c2=9 and that solve the puzzle.

Regards, Carcul
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Postby angusj » Thu Jan 26, 2006 10:24 pm

barbe rouge wrote:Also the Simple Sudoku that I use, does not gine any hint on this position, which I find it a little perplexing,
if it is colouring, since it uses colours.

No, SudoCue is not using the 'coloring' technique, but I guess the cells have been colored simply to show you a hint.

There is a 'forcing chain' through the blue colored cells which will allow the 6 in the red cell to be excluded. Simple Sudoku does not show hints for forcing chains.
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Postby CathyW » Thu Jan 26, 2006 10:42 pm

angusj wrote:There is a 'forcing chain' through the blue colored cells which will allow the 6 in the red cell to be excluded.


Looks like my attempt at multi-colouring was a "happy coincidence" then rather than a legitimate method of making that exclusion.

Angus - was your chain different to Carcul's?
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Postby angusj » Thu Jan 26, 2006 11:16 pm

CathyW wrote:Angus - was your chain different to Carcul's?

Yes.
Either r4c5 = 6 or r7c3 = 6 because
a. r4c5<>6 => r5c6=6 => r5c8<>6 => r9c8=6 => r9c1<>6 => r7c3=6
b. r7c3<>6 => r9c1=6 => r9c8 <> 6 => r5c8=6 => r5c6<>6 => r4c5=6

Image
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Postby barbe rouge » Fri Jan 27, 2006 12:03 am

CathyW,
http://www.sudocue.net/olddaily.php?id=38&sol=0

angusj,
your solution is much easier for me since it is similar
with sandmans xy chains. However I have one question since
i'm not familiar with cells that have three possibilities.
When from the chain the r5c8 becomes a 7 then r9c8 has to
be a 6 since there is no other 6 in the c8.
If in c8 was another cell that had the choice of a 6
apart from r5c8 and r9c8 could you still move from r5c8 to
r9c8?

Carcul,
if i understand well your answer to the above question
is that it is possible, since you continue from r4c7 to
r6c7 and to r5c8, right?
Also could you please verify and explain the symbols below?
"=x=" -> "is not x, then" ?
"-x-" -> "is x, then" ?
"|" -> ?
"(...)" -> ?



CathyW, Carcul, angusj,
thank you very much:D
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Postby tarek » Fri Jan 27, 2006 12:42 am

Carcul wrote:However, this chain does not solve the puzzle


The following also does not solve it in one step, but I think it provides a better chain to start with, & it develops a very interesting puzzle.
Code: Select all
*--------------------------------------------------------*
| 456   368   3468 | 9     1     7    | 2     58    346  |
| 456   1     4689 | 3     46    2    | 578   578   469  |
| 2     369   7    | 8     5     46   | 36    1     3469 |
|------------------+------------------+------------------|
| 8     69    169  | 7     46    5    | 146   3     2    |
| 3     2     5    | 1     9     46   | 467   67    8    |
| 7     4     16   | 2     3     8    | 16    9     5    |
|------------------+------------------+------------------|
| 1     5     46   | 46    8     3    | 9     2     7    |
| 9     7     38   | 56    2     1    | 3568  4     36   |
| 46    38    2    | 456   7     9    | 3568  568   1    |
*--------------------------------------------------------*
Candidates in r4c7 will force r3c7 to have only 3 as valid Candidates
r4c7=1: r4c7=1 => r6c7=6 => r3c7=3
r4c7=4: r4c7=4 => r4c5=6 => r5c6=4 => r3c6=6 => r3c7=3
r4c7=6: r4c7=6 => r3c7=3
Threfore r3c7=3
*-----------------------------------------------*
| 46   8    3   | 9    1    7   | 2    5    46  |
| 5    1    469 | 3    46   2   | 78   78   469 |
| 2    69   7   | 8    5    46  | 3    1    469 |
|---------------+---------------+---------------|
| 8    69   169 | 7    46   5   | 146  3    2   |
| 3    2    5   | 1    9    46  | 467  67   8   |
| 7    4    16  | 2    3    8   | 16   9    5   |
|---------------+---------------+---------------|
| 1    5    46  | 46   8    3   | 9    2    7   |
| 9    7    8   | 56   2    1   | 56   4    3   |
| 46   3    2   | 456  7    9   | 568  68   1   |
*-----------------------------------------------*
Eliminating 6 From r2c3 (Swordfish in Rows 678)
Eliminating 6 From r4c3 (Swordfish in Rows 678)
Eliminating 6 From r9c4 (Swordfish in Rows 678)
Eliminating 6 From r4c7 (Swordfish in Rows 678)
Eliminating 6 From r5c7 (Swordfish in Rows 678)
Eliminating 6 From r9c7 (Swordfish in Rows 678)
*-----------------------------------------------*
| 46   8    3   | 9    1    7   | 2    5    46  |
| 5    1    49  | 3    46   2   | 78   78   469 |
| 2    69   7   | 8    5    46  | 3    1    469 |
|---------------+---------------+---------------|
| 8    69   19  | 7    46   5   | 14   3    2   |
| 3    2    5   | 1    9    46  | 47   67   8   |
| 7    4    16  | 2    3    8   | 16   9    5   |
|---------------+---------------+---------------|
| 1    5    46  | 46   8    3   | 9    2    7   |
| 9    7    8   | 56   2    1   | 56   4    3   |
| 46   3    2   | 45   7    9   | 58   68   1   |
*-----------------------------------------------*
Eliminating 6 From r3c6 (4 & 9 in r2c3 form an XY wing with 6 in r2c5 & r3c2)

& that solves it
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Postby angusj » Fri Jan 27, 2006 1:13 am

barbe rouge wrote:If in c8 was another cell that had the choice of a 6
apart from r5c8 and r9c8 could you still move from r5c8 to
r9c8?

No.
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Postby ronk » Fri Jan 27, 2006 2:23 am

angusj wrote:There is a 'forcing chain' through the blue colored cells which will allow the 6 in the red cell to be excluded. Simple Sudoku does not show hints for forcing chains.

It looks like single digit multi-coloring to me. Instead of being 5-sided turbot fish with 2 strong links (connected by a weak link), this one is 7-sided with 3 strong links (alternately connected by two weak links).
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Postby barbe rouge » Fri Jan 27, 2006 2:58 am

tarek,
nice solution, thanks for sharing.

angusj,
one more question please. When Simple Sudoku says
that a puzzle is assymetrical what does it mean?

ronk,
could you please be a little bit more analytical by
defining the cells?

Since I have drawn your attention with this puzzle, let me
ask something else. How do you come up to these solutions
when searching for chains?
Do you search randomly, you have a pattern, are there some
clues you take into account before you start searching and
what are they? Thanks to all:D
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Postby angusj » Fri Jan 27, 2006 3:25 am

ronk wrote:It looks like single digit multi-coloring to me.

Yes, the chain is made up of 3 conjugate pairs so you are correct. However, I doubt that many would spot this without help.
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Postby ronk » Fri Jan 27, 2006 3:29 am

barbe rouge wrote:could you please be a little bit more analytical by defining the cells?

I was referring to the cells in Angus' illustration here.
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