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Daily Telegraph May 15, 2015

 
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Clement



Joined: 24 Apr 2006
Posts: 980
Location: Dar es Salaam Tanzania

PostPosted: Mon May 18, 2015 5:56 pm    Post subject: Daily Telegraph May 15, 2015 Reply with quote

Code:

+-------+-------+-------+
| . 5 7 | 1 . 2 | 9 . . |
| . 8 . | 3 . . | 7 . . |
| . . . | . . . | . 1 5 |
+-------+-------+-------+
| 3 . . | . 4 . | . . 9 |
| . . . | 2 . 7 | . . . |
| 5 . . | . 9 . | . . 2 |
+-------+-------+-------+
| 8 6 . | . . . | . . . |
| . . 1 | . . 6 | . 4 . |
| . . 5 | 9 . 1 | 2 6 . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Mon May 18, 2015 8:05 pm    Post subject: Reply with quote

Code:

+-----------+------------+-------------+
| 46 5  7   | 1   68  2  | 9   38 3468 |
| 1  8  469 | 3   56  59 | 7   2  46   |
| 2  3  69  | 4   7   89 | 68  1  5    |
+-----------+------------+-------------+
| 3  17 2   | 568 4   58 | 168 78 9    |
| 46 9  8   | 2   1   7  | 346 5  36   |
| 5  17 46  | 68  9   3  | 146 78 2    |
+-----------+------------+-------------+
| 8  6  3   | 7   2   4  | 5   9  1    |
| 9  2  1   | 58  358 6  | 38  4  7    |
| 7  4  5   | 9   38  1  | 2   6  38   |
+-----------+------------+-------------+

Play this puzzle online at the Daily Sudoku site

XY-Chain:

(8=6)r1c5-(6=4)r1c1-(4=6)r5c1-(6=3)r5c9-(3=8)r9c9=>r9c5<>8
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Clement



Joined: 24 Apr 2006
Posts: 980
Location: Dar es Salaam Tanzania

PostPosted: Tue May 19, 2015 8:50 am    Post subject: Daily Telegraph May 15, 2015 Reply with quote

Code:

+-----------+------------+------------+
| 46 5  7   | 1   68  2  | 9   3  468 |
| 1  8  469 | 3   56  59 | 7   2  46  |
| 2  3  69  | 4   7   89 | 68  1  5   |
+-----------+------------+------------+
| 3  17 2   | 568 4   58 | 16  78 9   |
| 46 9  8   | 2   1   7  | 346 5  36  |
| 5  17 46  | 68  9   3  | 146 78 2   |
+-----------+------------+------------+
| 8  6  3   | 7   2   4  | 5   9  1   |
| 9  2  1   | 58  358 6  | 38  4  7   |
| 7  4  5   | 9   38  1  | 2   6  38  |
+-----------+------------+------------+
XY-Wing 89-6 pivot in r3c6; r1c1<6> stte
Also the chain (6=4)r2c9-r2c3=r1c1-(4=6)r5c1 => -6r5c9.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Tue May 19, 2015 2:17 pm    Post subject: Reply with quote

Code:
|*46 5  7   | 1   68  2  | 9   38*3468 |
| 1  8 *469 | 3   56  59 | 7   2 *46   |
| 2  3  69  | 4   7   89 | 68  1  5    |
+-----------+------------+-------------+
| 3  17 2   | 568 4   58 | 168 78 9    |
|*46 9  8   | 2   1   7  |*346 5  36   |
| 5  17*46  | 68  9   3  |*146 78 2    |
+-----------+------------+-------------+
| 8  6  3   | 7   2   4  | 5   9  1    |
| 9  2  1   | 58  358 6  | 38  4  7    |
| 7  4  5   | 9   38  1  | 2   6  38


Another solution is the 8-cell AUR(46)r1c19,r2c39,r5c17,r6c37 with external inferences:
6r3c3 (for block 1)
6r3c7 (for block 3)
6r34c7 (for column 7)

6r3c3 => r1c1<>6
||
(6-8)r3c7=8r3c6-(8=6)r1c5 > r1c1<>6
||
(6-1)r4c7=(1-4)r6c7=4r6c3-(4=6)r5c1=> r1c1<>6
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Tue May 19, 2015 4:20 pm    Post subject: Reply with quote

Nice find, Ted. I haven't use externals yet due to lack of understanding. In your solution, why use r4c7 when r3c7 takes care of both box 3 and c7?
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Wed May 20, 2015 2:11 pm    Post subject: Reply with quote

Marty R. wrote:
In your solution, why use r4c7 when r3c7 takes care of both box 3 and c7?

Marty, when using externals you may select rows, columns or blocks but you must use ALL external inferences is that unit. All digits involved in the AUR must be resolved.

Digit 4 has no external inferences.

For Digit 6, I used the block to cover r1c1,r2c3 which has a single inference 6r3c3. For cells r12c9 I again used block which also had a single inference, 6r3c7. The block containing cells r5c1 and r6c3 does not have any external inferences so that is a obvious choice. Cells r56c7 has two external inferences for row (r5c9,r6c4), column (r34c7) and block (r4c7, r5c9). By selecting column, I only had one additional inference to resolve.

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Wed May 20, 2015 6:50 pm    Post subject: Reply with quote

Quote:
Marty, when using externals you may select rows, columns or blocks but you must use ALL external inferences is that unit. All digits involved in the AUR must be resolved.

Digit 4 has no external inferences.

For Digit 6, I used the block to cover r1c1,r2c3 which has a single inference 6r3c3. For cells r12c9 I again used block which also had a single inference, 6r3c7. The block containing cells r5c1 and r6c3 does not have any external inferences so that is a obvious choice. Cells r56c7 has two external inferences for row (r5c9,r6c4), column (r34c7) and block (r4c7, r5c9). By selecting column, I only had one additional inference to resolve.


Ok, Ted, Thank you. I did notice that there are no external 4s. I don't see r5c9 and r6c4 actually used in the solution.

Quote:
The block containing cells r5c1 and r6c3 does not have any external inferences so that is a obvious choice


This seems to imply that if that if there were external inferences they would need to be used. I thought only the polyvalue cells need to be covered because if they are true, the DP is broken?

Suppose we had a simple UR, such as the four cells r56c3 and r56c7. Could we proceed and say either rc7 or r5c9 MUST be true?
Code:
|*46 5  7   | 1   68  2  | 9   38*3468 |
| 1  8 *469 | 3   56  59 | 7   2 *46   |
| 2  3  69  | 4   7   89 | 68  1  5    |
+-----------+------------+-------------+
| 3  17 2   | 568 4   58 | 168 78 9    |
|*    9 46   | 2   1   7  |*346 5  36   |
| 5  17*46  | 68  9   3  |*146 78 2    |
+-----------+------------+-------------+
| 8  6  3   | 7   2   4  | 5   9  1    |
| 9  2  1   | 58  358 6  | 38  4  7    |
| 7  4  5   | 9   38  1  | 2   6  38   [/code
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Thu May 21, 2015 1:56 pm    Post subject: Reply with quote

Marty R. wrote:
Quote:
Marty, when using externals you may select rows, columns or blocks but you must use ALL external inferences is that unit. All digits involved in the AUR must be resolved.

Digit 4 has no external inferences.

For Digit 6, I used the block to cover r1c1,r2c3 which has a single inference 6r3c3. For cells r12c9 I again used block which also had a single inference, 6r3c7. The block containing cells r5c1 and r6c3 does not have any external inferences so that is a obvious choice. Cells r56c7 has two external inferences for row (r5c9,r6c4), column (r34c7) and block (r4c7, r5c9). By selecting column, I only had one additional inference to resolve.


Ok, Ted, Thank you. I did notice that there are no external 4s. I don't see r5c9 and r6c4 actually used in the solution.

Quote:
The block containing cells r5c1 and r6c3 does not have any external inferences so that is a obvious choice


This seems to imply that if that if there were external inferences they would need to be used. I thought only the polyvalue cells need to be covered because if they are true, the DP is broken?

Suppose we had a simple UR, such as the four cells r56c3 and r56c7. Could we proceed and say either rc7 or r5c9 MUST be true?
Code:
|*46 5  7   | 1   68  2  | 9   38*3468 |
| 1  8 *469 | 3   56  59 | 7   2 *46   |
| 2  3  69  | 4   7   89 | 68  1  5    |
+-----------+------------+-------------+
| 3  17 2   | 568 4   58 | 168 78 9    |
|*    9 46   | 2   1   7  |*346 5  36   |
| 5  17*46  | 68  9   3  |*146 78 2    |
+-----------+------------+-------------+
| 8  6  3   | 7   2   4  | 5   9  1    |
| 9  2  1   | 58  358 6  | 38  4  7    |
| 7  4  5   | 9   38  1  | 2   6  38   [/code


Marty, when using externals you may select rows, columns or blocks but you must use ALL external inferences is that row, column or block. For r56c7, I used column thus r5c9 and r6c4 were never used. I could have used rows for both r56c7 with external references r5c9 and r6c4 respectively but that seemed more work that using c7. Note that I could have mixed inferences by using the internal inferences for r56c7:
3r5c7-(3=6)r5c9-(6=8)r21c9-(8=6)r1c5 => r1c1<6> r1c1<>6
(1-4)r6c4=4r6c3-(4=6)r5c1 => r1c1<>6

You are correct that only polyvalued cells need to be covered. Non-polyvalued cells basically form lock sets that eliminate any external inferences.

Your example has a typo, rc7, so I am not sure what cell you intended. If you are using block inferences then either 6r4c7 or 6r5c9 must be true since the block only contains those two inferences.
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