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An ER Loop

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Asellus

Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

Posted: Mon Aug 06, 2007 9:28 pm Post subject: An ER Loop

I came across this recently:

Code:

+------------+-------+------------+
| 1 67 8 | 9 3 4 | 56 567 2 |
| 9 2 47 | 1 5 6 | 47 3 8 |
| 5 3 46 | 7 2 8 | 9 46 1 |
+------------+-------+------------+
| 46 569 3 | 2 1 7 | 8 69 45 |
| 8 567 267 | 3 4 9 | 26 1 57 |
| 24 79 1 | 6 8 5 | 3 29 47 |
+------------+-------+------------+
| 3 1 5 | 8 9 2 | 47 47 6 |
| 26 4 26 | 5 7 3 | 1 8 9 |
| 7 8 9 | 4 6 1 | 25 25 3 |
+------------+-------+------------+

The <6> at R5C3 can be eliminated in a number of ways, including a Color Wing and a Finned Swordfish.

It can also be eliminated using ERs in Boxes 1 and 3 and the strong link in Box 6:

Code:

+-------------+-------+------------+
| 1 67 8 | 9 3 4 | 56 567 2 |
|e9 e2 47 | 1 5 6 |e47 3 e8 |
|e5 e3 46 | 7 2 8 |e9 46 e1 |
+-------------+-------+------------+
| 46 569 3 | 2 1 7 | 8 6r9 45 |
| 8 567 2-67 | 3 4 9 | 26g 1 57 |
| 24 79 1 | 6 8 5 | 3 29 47 |
+-------------+-------+------------+
| 3 1 5 | 8 9 2 | 47 47 6 |
| 26 4 26 | 5 7 3 | 1 8 9 |
| 7 8 9 | 4 6 1 | 25 25 3 |
+-------------+-------+------------+

However, note that Box 6 is itself an ER on <6>. This forms an "ER Loop":

Code:

+-------------+-------+------------+
| 1 67 8 | 9 3 4 | 56 567 2 |
|e9 e2 47 | 1 5 6 |e47 3 e8 |
|e5 e3 46 | 7 2 8 |e9 46 e1 |
+-------------+-------+------------+
| 46 569 3 | 2 1 7 |e8 69 e45 |
| 8 567 2-67 | 3 4 9 | 26 1 57 |
| 24 79 1 | 6 8 5 |e3 29 e47 |
+-------------+-------+------------+
| 3 1 5 | 8 9 2 | 47 47 6 |
| 26 4 26 | 5 7 3 | 1 8 9 |
| 7 8 9 | 4 6 1 | 25 25 3 |
+-------------+-------+------------+

As it happens, the candidate <6> in R5C3 can "see itself" in this ER Loop "mirror," which is not logically permissible and is thus another means of elimination.

I'd never encountered this before. Perhaps others have? In any case, I thought it was cool.

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