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Puzzle 11/02/11

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Fri Feb 11, 2011 5:07 pm    Post subject: Puzzle 11/02/11 Reply with quote
Code:
 +-----------------------+
 | 9 . . | . . . | 1 6 . |
 | . 6 . | . 9 1 | 3 8 . |
 | . . 1 | . 6 . | . . . |
 |-------+-------+-------|
 | . . . | . 3 8 | . 2 . |
 | . 2 8 | 9 5 . | 4 7 3 |
 | . 3 . | 1 . . | . . 5 |
 |-------+-------+-------|
 | 2 1 . | . 8 . | 9 . . |
 | 4 9 . | 6 2 . | . 1 . |
 | . . . | . 1 9 | . . 2 |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK
PostPosted: Fri Feb 11, 2011 5:56 pm    Post subject: Reply with quote
Valid MUG?
Code:
 *-----------------------------------------------------------*
 | 9     58    25-3  | 2358  47    35    | 1     6     47    |
 | 57    6     2457  | 2457  9     1     | 3     8     47    |
 | 38    478   1     | 3478  6     347   | 2     5     9     |
 |-------------------+-------------------+-------------------|
 | 57    457   9     | 47    3     8     | 6     2     1     |
 | 1     2     8     | 9     5     6     | 4     7     3     |
 | 6     3     47    | 1     47    2     | 8     9     5     |
 |-------------------+-------------------+-------------------|
 | 2     1    *57+3  |*3457  8     3457  | 9    *34    6     |
 | 4     9    *57+3  | 6     2     357   |*57    1     8     |
 | 8-3   578   6     |*3457  1     9     |*57   *34    2     |
 *-----------------------------------------------------------*

A UR(34)r79c48 overlapping a 6-cell ADP(57)r7c34|r8c37|r9c47 to make a MUG(3457).

So two steps...
Code:
Type-2 MUG(3457) ; r9c1<>3, r1c3<>3
w-wing(57) r2c1, r9c2, (5)r4c1=r4c2 ; r3c2<>7
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sat Feb 12, 2011 5:28 am    Post subject: Reply with quote
I used Multi-Coloring on 7 and two XY-Wings, 583 and 358
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sat Feb 12, 2011 12:40 pm    Post subject: Reply with quote
peterj wrote:
Valid MUG?
Code:
 *-----------------------------------------------------------*
 | 9     58    25-3  | 2358  47    35    | 1     6     47    |
 | 57    6     2457  | 2457  9     1     | 3     8     47    |
 | 38    478   1     | 3478  6     347   | 2     5     9     |
 |-------------------+-------------------+-------------------|
 | 57    457   9     | 47    3     8     | 6     2     1     |
 | 1     2     8     | 9     5     6     | 4     7     3     |
 | 6     3     47    | 1     47    2     | 8     9     5     |
 |-------------------+-------------------+-------------------|
 | 2     1    *57+3  |*3457  8     3457  | 9    *34    6     |
 | 4     9    *57+3  | 6     2     357   |*57    1     8     |
 | 8-3   578   6     |*3457  1     9     |*57   *34    2     |
 *-----------------------------------------------------------*

A UR(34)r79c48 overlapping a 6-cell ADP(57)r7c34|r8c37|r9c47 to make a MUG(3457).


Peter: I'm not comfortable with the fact that r78c3<>3 results in r8c37=57 forcing r8c6=3 ... and destroying the <34> UR.

However, here's a 10-cell <47> DP for you to play with! (darn dangling participle!!!) _ Laughing

Code:
 +--------------------------------------------------------------+
 |  9     58    235   |  2358 *47    35    |  1     6    *47    |
 |  57    6    *47+25 |  2457  9     1     |  3     8    *47    |
 |  38   *47+8  1     | *47+38 6     347   |  2     5     9     |
 |--------------------+--------------------+--------------------|
 |  57   *45+7  9     | *47    3     8     |  6     2     1     |
 |  1     2     8     |  9     5     6     |  4     7     3     |
 |  6     3    *47    |  1    *47    2     |  8     9     5     |
 |--------------------+--------------------+--------------------|
 |  2     1     357   |  3457  8     3457  |  9     34    6     |
 |  4     9     357   |  6     2     357   |  57    1     8     |
 |  38    578   6     |  3457  1     9     |  57    34    2     |
 +--------------------------------------------------------------+
 # 53 eliminations remain

Regards, Danny

Last edited by daj95376 on Sat Feb 12, 2011 1:01 pm; edited 1 time in total
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK
PostPosted: Sat Feb 12, 2011 1:00 pm    Post subject: Reply with quote
daj95376 wrote:
Peter: I'm not comfortable with the fact that r78c3<>3 results in r8c37=57 forcing r8c6=3 ... and destroying the <34> UR.

Yes it destroys the UR(34) ... but doesn't it also force the DP(57)?

r78c3<>3 creates two NP(57) r8c37 and r78c3...
(57)r8c37 forces 3 in r8c6 hence r79c4<>3...
(57)r78c3 forces 4 in r6c3 and so 4 in r4c4 hence r79c4<>4

We now have the DP(57)!

I find these MUGs endlessley confusing and the recent thread on the sudoku.org.uk board didn't help. I was hoping that "overlapping UR" was a good starting point.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sat Feb 12, 2011 1:28 pm    Post subject: Reply with quote
If I start the <34> UR with r7c8=3 and the <57> DP with r8c7=5, then I can't complete cells r7c46 in [band 3] of your MUG.

Code:
 *-----------------------------------------------------------*
 | 9     5     23    | 238   47    5     | 1     6     47    |
 | 57    6     24    | 247   9     1     | 3     8     47    |
 | 8     47    1     | 3478  6     47    | 2     5     9     |
 |-------------------+-------------------+-------------------|
 | 57    457   9     | 47    3     8     | 6     2     1     |
 | 1     2     8     | 9     5     6     | 4     7     3     |
 | 6     3     4     | 1     47    2     | 8     9     5     |
 |-------------------+-------------------+-------------------|
 | 2     1     5     | 47    8     47    | 9     3     6     |
 | 4     9     7     | 6     2     3     | 5     1     8     |
 | 3     8     6     | 5     1     9     | 7     4     2     |
 *-----------------------------------------------------------*
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ronk



Joined: 07 May 2006
Posts: 398
PostPosted: Sat Feb 12, 2011 2:11 pm    Post subject: Reply with quote
I suspect any 2-cell overlap of two BUG-Lites** will not result in a MUG. In this case, the pattern ...

Code:
 .   .   .   | .    .   .   | .   .   .   
-------------+--------------+--------------
 .   .   57  | 3457 .   .   | .   34  .   
 .   .   57  | .    .   .   | 57  .   .   
 .   .   .   | 3457 .   .   | 57  34  .   

... has ...

Code:
 .   .   .   | .    .   .   | .   .   .   
-------------+--------------+--------------
 .   .   7   | 3    .   .   | .   4   .   
 .   .   5   | .    .   .   | 7   .   .   
 .   .   .   | 7    .   .   | 5   3   .   

... as a possible outcome. No deadly pattern there.

** A UR is the smallest possible BUG-Lite+0.
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK
PostPosted: Sat Feb 12, 2011 2:19 pm    Post subject: Reply with quote
ronk wrote:
I suspect any 2-cell overlap of two BUG-Lites** will not result in a MUG..

Do you think the converse is true i.e any 1-cell overlap of two BUG-lites/UR is a MUG is true? At least I can come out of this with some sort of 'rule' to work from in the future!
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ronk



Joined: 07 May 2006
Posts: 398
PostPosted: Sat Feb 12, 2011 6:52 pm    Post subject: Reply with quote
peterj wrote:
ronk wrote:
I suspect any 2-cell overlap of two BUG-Lites** will not result in a MUG..

Do you think the converse is true i.e any 1-cell overlap of two BUG-lites/UR is a MUG is true?

Yes. Consider the outcome for each possible placement in the overlap-cell ... in the absence of an "extra" candidate anywhere in the combined pattern, of course.
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