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Free Press May 10, 2013

 
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Sat May 11, 2013 2:44 pm    Post subject: Free Press May 10, 2013 Reply with quote

Not yet started ...
Code:
Puzzle: FP051013
+-------+-------+-------+
| . . . | . 1 . | . 8 . |
| 6 . . | . . 7 | . . . |
| . 2 5 | 6 . 9 | . . 4 |
+-------+-------+-------+
| 4 . . | . . . | 2 . . |
| 2 . . | 4 3 5 | . . 9 |
| . . 9 | . . . | . . 1 |
+-------+-------+-------+
| 5 . . | 8 . 1 | 7 9 . |
| . . . | 2 . . | . . 3 |
| . 1 . | . 5 . | . . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Keith
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arkietech



Joined: 31 Jul 2008
Posts: 1723
Location: Northwest Arkansas USA

PostPosted: Sat May 11, 2013 5:27 pm    Post subject: Reply with quote

after a 462 xy-wing removing a 2 from r2c9 I wound up here:
Code:
 *-----------------------------------------------------------*
 | 39    349   7     | 5     1     24    | 69    8     26    |
 | 6     489  b48    | 3     24    7     | 19    12    5     |
 | 1     2     5     | 6     8     9     | 3     7     4     |
 |-------------------+-------------------+-------------------|
 | 4     3568 b368   | 1     9     68    | 2    a35    7     |
 | 2     7     1     | 4     3     5     | 8     6     9     |
 | 38    3568  9     | 7     26    268   |a45    35-4  1     |
 |-------------------+-------------------+-------------------|
 | 5     346   2346  | 8     46    1     | 7     9     26    |
 | 89    4689 b468   | 2     7     46    | 15    15    3     |
 | 7     1    c26    | 9     5     3     | 6-4  c24    8     |
 *-----------------------------------------------------------*
(4=3)r4c8,r6c7-(3=486)r248c3-(6=4)r9c38 => -4r9c7,r6c8; ste
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JC Van Hay



Joined: 13 Jun 2010
Posts: 370
Location: Charleroi, Belgium

PostPosted: Sat May 11, 2013 6:24 pm    Post subject: Reply with quote

#1. 18 Singles
Code:
+------------------+----------------+------------------+
| 39  349     7    | 35  1     4(2) | 569   8    5(26) |
| 6   3489    348  | 35  4-2   7    | 159   125  25    |
| 1   2       5    | 6   8     9    | 3     7    4     |
+------------------+----------------+------------------+
| 4   38(56)  368  | 1   9     68   | 2     35   7     |
| 2   7       1    | 4   3     5    | 8     6    9     |
| 38  38(56)  9    | 7   (26)  68-2 | (45)  345  1     |
+------------------+----------------+------------------+
| 5   34(6)   2346 | 8   4(6)  1    | 7     9    2(6)  |
| 89  489(6)  468  | 2   7     4(6) | 1456  145  3     |
| 7   1       246  | 9   5     3    | (46)  24   8     |
+------------------+----------------+------------------+
#2. Chain[8] : 2r1c6=(2-6)r1c9=6r7c9-[6r7c2 and 6r7c5=6r8c6-6r8c2 and (6=4)r9c7-(4=5)r6c7-5r6c2=(5-6)r4c2]=6r6c2-(6=2)r6c5 :=> -2r2c5.r6c6; ste

Note : the chain can also be written as a Kraken Column 6C2.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Sun May 12, 2013 1:00 am    Post subject: Reply with quote

This was a tough nut to crack. I used a chain which eliminated 8 from r4c23 and r6c6, leaving me here, where I then needed another chain.

Code:

+--------------+----------+------------+
| 39 349  7    | 35 1  24 | 69 8   256 |
| 6  3489 348  | 35 24 7  | 19 12  25  |
| 1  2    5    | 6  8  9  | 3  7   4   |
+--------------+----------+------------+
| 4  356  36   | 1  9  8  | 2  35  7   |
| 2  7    1    | 4  3  5  | 8  6   9   |
| 38 358  9    | 7  26 26 | 45 345 1   |
+--------------+----------+------------+
| 5  346  2346 | 8  46 1  | 7  9   26  |
| 89 4689 468  | 2  7  46 | 15 15  3   |
| 7  1    26   | 9  5  3  | 46 24  8   |
+--------------+----------+------------+

Play this puzzle online at the Daily Sudoku site

(6=3)r4c3-(3=5)r4c8-(5=1)r8c8-(125=6)r2c89r1c9-r7c9=6r9c7=>r9c3<>6
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Leren



Joined: 13 May 2013
Posts: 5

PostPosted: Mon May 13, 2013 10:07 pm    Post subject: Reply with quote

Code:
*--------------------------------------------------------------*
| 39   d349   7      | 35    1    c24     | 69    8    h256    |
| 6     3489  348    | 35   b24    7      | 19    12    5-2    |
| 1     2     5      | 6     8     9      | 3     7     4      |
|--------------------+--------------------+--------------------|
| 4     3568  368    | 1     9     68     | 2     35    7      |
| 2     7     1      | 4     3     5      | 8     6     9      |
| 38    3568  9      | 7     26    268    | 45    345   1      |
|--------------------+--------------------+--------------------|
| 5    e36-4 f24-36  | 8    a46    1      | 7     9    g26     |
| 89    4689  468    | 2     7     46     | 15    15    3      |
| 7     1     26     | 9     5     3      | 46    24    8      |
*--------------------------------------------------------------*

*(4) r7c5 = r2c5 - r1c6 = r1c2 - r7c2 =* (4-2) r7c3 = r7c9 - r1c9 = r1c6 loop => -4 r7c2, -36 r7c3, -2 r2c9; stte

Leren
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Sun Jun 02, 2013 1:53 pm    Post subject: Reply with quote

After basics:
Code:
+----------------+----------------+----------------+
| 39  *349  7    | 35   1   *24   | 69   8    256  |
| 6    3489 348  | 35 *C24   7    | 19   12  -25   |
| 1    2    5    | 6    8    9    | 3    7    4    |
+----------------+----------------+----------------+
| 4    3568 368  | 1    9    68   | 2    35   7    |
| 2    7    1    | 4    3    5    | 8    6    9    |
| 38   3568 9    | 7   B26   268  | 45   345  1    |
+----------------+----------------+----------------+
| 5  3-4-6 234-6 | 8  *D46   1    | 7    9   A26   |
| 89   4689 468  | 2    7    46   | 15   15   3    |
| 7    1    26   | 9    5    3    | 46   24   8    |
+----------------+----------------+----------------+

M-wing: If A is 6 B is 6. Extending 2 to C, R2C9<>2. (This is also an XY-wing ACD.)

M-wing: If A is 2 B is 2. Extending 6 to D, R7C23<>6.

SS on 4 in R1C5. R7C2<>4.

Keith
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JC Van Hay



Joined: 13 Jun 2010
Posts: 370
Location: Charleroi, Belgium

PostPosted: Sun Jun 02, 2013 6:27 pm    Post subject: Reply with quote

Leren wrote:
Code:
*--------------------------------------------------------------*
| 39   d349   7      | 35    1    c24     | 69    8    h256    |
| 6     3489  348    | 35   b24    7      | 19    12    5-2    |
| 1     2     5      | 6     8     9      | 3     7     4      |
|--------------------+--------------------+--------------------|
| 4     3568  368    | 1     9     68     | 2     35    7      |
| 2     7     1      | 4     3     5      | 8     6     9      |
| 38    3568  9      | 7     26    268    | 45    345   1      |
|--------------------+--------------------+--------------------|
| 5    e36-4 f24-36  | 8    a46    1      | 7     9    g26     |
| 89    4689  468    | 2     7     46     | 15    15    3      |
| 7     1     26     | 9     5     3      | 46    24    8      |
*--------------------------------------------------------------*

*(4) r7c5 = r2c5 - r1c6 = r1c2 - r7c2 =* (4-2) r7c3 = r7c9 - r1c9 = r1c6 loop => -4 r7c2, -36 r7c3, -2 r2c9; stte

Leren
Hi Leren, I missed your post for some time Sad
Nice catch ! But ... Your chain as it is written is not an explicit loop and only eliminates 4r7c2 as it contains Kite(4R1C5) :=> -4r7c2!
To get "the loop", the simplest thing to do is to use 4B2 instead of 4C5 as follows :
    2r7c3=2r7c9-2r1c9=(2-4)r1c6=[4r1c2-4r7c2 and 4r2c5-4r7c5]=4r7c3 @
    or, in reverse order,
    4r7c3=[4r7c2-4r1c2 or 4r7c5-4r2c5]=(4-2)r1c6=2r1c9-2r7c9=2r7c3 @
    :=> -2r2c9,r7c3=24(:=>r7c2=3 ... "->-4r7c2")
Note : Only the "true" weak links outside the "brackets" become strong, as the loop only requires the derived SIS 4r1c6=4r7c3.

Regards, JC
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oaxen



Joined: 10 Jul 2006
Posts: 96

PostPosted: Mon Jun 03, 2013 9:22 am    Post subject: Reply with quote

Of all the available bivalues, 2 in column 8 seems to be most interesting. A quick check gives 8 must-bees independent of which one of the 2īs. one chooses
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aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Mon Jun 03, 2013 12:38 pm    Post subject: Reply with quote

JC Van Hay

Or thinking in base/cover/rank terms
it's a rank 1 structure => not a loop
ie
Base
4 truths : 2r7 2r1 4r1 4r7
Cover :
5 truths : 2c9 r1c6 4c2 r7c3 + 4r7c5
Rank = 5-4=1.

Logic then becomes :
4r7c5 false =>rank 0 =>loop =><2>r2c9 <4>r18c2 <36>r7c3
4r7c5 true => -(4=2)r2c5-2r1c6=2r1c9 =><2>r2c9 (2-36)r7c3
Hence what is common is eliminated : <2>r2c9 <36>r7c3
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JC Van Hay



Joined: 13 Jun 2010
Posts: 370
Location: Charleroi, Belgium

PostPosted: Mon Jun 03, 2013 7:01 pm    Post subject: Reply with quote

Aran

Nice interpretation while using non-overlapping truths!

On my side, I may be improperly called loops the chains I wrote all the more since their ranks are undefined due to overlapping truths.
Nonetheless, the rank 0 links were clearly identified which is not so easy in the more general cases !
And I don't speak, as you know, of the different needed "chains" to explain each group of eliminations !
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aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Thu Jun 06, 2013 10:44 am    Post subject: Reply with quote

JC Van Hay wrote:
Aran

On my side, I may be improperly called loops the chains I wrote all the more since their ranks are undefined due to overlapping truths.

Insofar as it has the form x=.......=y-x it's a loop
Insofar as it has rank 1, it's not a loop...
Au choix !

Just out of interest, switching to uniqueness
Code:

 *-----------------------------------------------------------*
 | 39    349   7     | 35    1     24    | 69    8     256   |
 | 6     3489  348   | 35    24    7     | 19    12    25    |
 | 1     2     5     | 6     8     9     | 3     7     4     |
 |-------------------+-------------------+-------------------|
 | 4     3568  368   | 1     9     68    | 2     35    7     |
 | 2     7     1     | 4     3     5     | 8     6     9     |
 | 38    3568  9     | 7     26    268   | 45    345   1     |
 |-------------------+-------------------+-------------------|
 | 5     346   2346  | 8     46    1     | 7     9     26    |
 | 89    4689  468   | 2     7     46    | 15    15    3     |
 | 7     1     26    | 9     5     3     | 46    24    8     |
 *-----------------------------------------------------------*

UR48r28c23 = sis {4r2c5 4r8c6 89r8c12}
DP893r816c12 = sis {4r1c2 56r6c2}
=>UR48 = sis {4r2c5 4r8c6 4r1c2 56r6c2}
4r2c5 4r8c6 4r1c2 =>r1c6=2
6r6c2-(6=2)r6c5-r2c5=2r1c6
5r6c2-(5=4)r6c7-(4=6)r9c7-r1c7=(6-2)r1c9=2r1c6
=>r1c6=2 ste
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