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Bud
Joined: 06 May 2010 Posts: 47 Location: Tampa, Florida
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Posted: Fri Sep 10, 2010 9:13 pm Post subject: 2 Digit 6 Cell AIC Continuous Loop 2 Examples |
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I am presenting this as a simple pattern technique rather than an AIC since it is such an easy pattern to spot. It consists of 2 single digit AIC's which are connected together at both ends. In this example, the pattern is both a 4 and an 8 2-string kite with cells labeled *. It is easy to show that the cells r1c7 and r9c3 in which the 4 and 8 AIC's are merged must be either 4 or 8. Hence the 235 cell eliminations. The 4 cell elimination in r7c9 is a continuous loop cell elimination.
Edit: I initially thought that this might be a type of M-Ring but the two 48 cells (r1c4 and r9c3) in the continuous loop are conjugate pairs rather than twin pairs as in an M-Ring. Therefore I now I think that this should be classified as a hidden W-Ring.
Since there are 4 distinct forms of a single digit 4 cell AIC's and since the two 4 cell AIC's do not have to be the same form, I count 16 different forms for this type of W-Ring.
2 Digit 6 Cell Continuous Loop #1 Code: |
+------------------+-------------------+--------------------+
| 28* 3 9 | 5 246 7 | -248* 1 246 |
| 4 5 1 | 68 2689 269 | 2379 3689 23679 |
| 7 6 28* | 3 1249 129 | 5 89 249 |
+------------------+-------------------+--------------------+
| 13569 8 356 | 167 1369 4 | 379 2 135679 |
| 12369 149 2346 | 1678 5 369 | 3789 3689 13679 |
| 13569 7 356 | 2 13689 1369 | 389 4 13569 |
+------------------+-------------------+--------------------+
| 1356 14 7 | 146 136 8 | 2349* 359 23-49 |
| 3569 49 3456 | 46 236 2356 | 1 7 8 |
| 1358 2 -34-58*| 9 7 135 | 6 35 34* |
+------------------+-------------------+--------------------+ |
The original puzzle is Sudoku.com.au 1-11-10 daily tough. I used basic moves and a 148 AIC to reach this point in the puzzle.
I have added a second example which consist of a 6 2-string kite and an 8 (normally useless) 4-cell row AIC which are connected together at the cells r8c1 and r3c5. This means that both of these cells must contain either 6 or 8. Hence the 347 cell eliminations. Also a 6 CL cell elimination occurs in r2c2.
2 Digit 6 Cell Continuous Loop #2 Code: |
+--------------------+----------------------+----------------------+
| 2347 8 457 | 137 137 379 | 23459 234579 6 |
| 367* 135-67 157 | 4 2 3679 | 8 3579 59 |
| 9 23467* 47 | 378* -36-78* 5 | 1 2347 24 |
+--------------------+----------------------+----------------------+
| 24 124 8 | 9 1456 246 | 7 2456 3 |
| 2347 123479 1479 | 12357 134567 23467 | 24569 24569 8 |
| 5 23479 6 | 237 347 8 | 249 249 1 |
+--------------------+----------------------+----------------------+
| 48 459 3 | 6 458 24 | 2459 1 7 |
|-46-78* 4567 2 | 3578* 9 1 | 3456 3456 45 |
| 1 45679 4579 | 2357 3457 2347 | 234569 8 2459 |
+--------------------+----------------------+----------------------+ |
The original puzzle is Sudoku.com.au 2-14-10 daily tough. I used only basic moves to reach this point in the puzzle. |
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