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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Fri Sep 24, 2010 5:46 pm Post subject: XY-Loop (again) |
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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 |
+------------+------------+----------+
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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: 3854
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| Posted: Fri Sep 24, 2010 6:49 pm Post subject: |
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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
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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
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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: 5770
Location: Rochester, NY, USA
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| Posted: Fri Sep 24, 2010 7:41 pm Post subject: |
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| 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. 
| 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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