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XY-Loop (again)

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5148
Location: Rochester, NY, USA

PostPosted: Fri Sep 24, 2010 5:46 pm    Post subject: XY-Loop (again) Reply with quote

I started a thread on this subject last November but I guess I didn't learn enough. My understanding is that a Loop is when an XY-Chain starts and ends in the same house. Supposedly, eliminations can be made for each number used. My problem is not knowing what eliminations to make. Below is Danny's puzzle 9-23 B.

Code:

+------------+------------+----------+
| 134 8  346 | 67  17 146 | 5   2 9  |
| 24  5  46  | 8   9  246 | 1   7 3  |
| 9   12 7   | 23  5  123 | 6   4 8  |
+------------+------------+----------+
| 247 3  249 | 1   6  8   | 79  5 24 |
| 57  14 8   | 359 2  39  | 379 6 14 |
| 125 6  29  | 359 4  7   | 39  8 12 |
+------------+------------+----------+
| 234 24 5   | 279 37 29  | 8   1 6  |
| 6   9  1   | 4   8  5   | 2   3 7  |
| 8   7  23  | 26  13 16  | 4   9 5  |
+------------+------------+----------+

Play this puzzle online at the Daily Sudoku site

Start with 3 in r9c3 and r9c5 and you can easily see where the chain ends in r9c4. I have already eliminated the 2 from r9c6.

Can a 2 be eliminated from c4? A 6 from b2? If yes, which ones and how is that determined?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Sep 24, 2010 6:49 pm    Post subject: Reply with quote

Here is your grid (before the elimination) and an XY-Loop containing your cells.

Code:
 +-----------------------------------------------------+
 |  134  8    346  | a67  b17   146  |  5    2    9    |
 |  24   5    46   |  8    9    246  |  1    7    3    |
 |  9    12   7    |  23   5    123  |  6    4    8    |
 |-----------------+-----------------+-----------------|
 |  247  3    249  |  1    6    8    |  79   5    24   |
 |  57   14   8    |  359  2    39   |  379  6    14   |
 |  125  6    29   |  359  4    7    |  39   8    12   |
 |-----------------+-----------------+-----------------|
 |  234  24   5    |  279  37   29   |  8    1    6    |
 |  6    9    1    |  4    8    5    |  2    3    7    |
 |  8    7   d23   | e26  c13   16-2 |  4    9    5    |
 +-----------------------------------------------------+
 # 49 eliminations remain

 (6=7)r1c4 - (7=1)r1c5 - (1=3)r9c5 - (3=2)r9c3 - (2=6)r9c4 - loop  =>  r9c6<>2

Instead of getting technical, I'm going to provide a "do this" answer.

* Look at each assignment and its corresponding elimination(s) in the loop.

* Delete that value from any cells that see the assignment and elimination cells.

Code:
loop_assignment   loop_elimination(s)    candidates that can be eliminated
---------------   -------------------    ---------------------------------

=7 r1c4           -7 r1c5                none
=1 r1c5           -1 r9c5                none
=3 r9c5           -3 r9c3                none
=2 r9c3           -2 r9c4                r9c6<>2
=6 r9c4           -6 r1c4 (from loop)    none

In loops more complicated than an XY-Loop, additional instructions would be necessary.

Regards, Danny
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Marty R.



Joined: 12 Feb 2006
Posts: 5148
Location: Rochester, NY, USA

PostPosted: Fri Sep 24, 2010 7:41 pm    Post subject: Reply with quote

Quote:
Instead of getting technical, I'm going to provide a "do this" answer.

Good. To use an ancient joke, getting technical with me is like telling a hair-raising story to a bald man. Laughing

Quote:
* Look at each assignment and its corresponding elimination(s) in the loop.

* Delete that value from any cells that see the assignment and elimination cells.

That's very clear and understandable. Thank you, I very much appreciate the help.
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