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2 Digit 6 Cell AIC Continuous Loop 2 Examples

 
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Bud



Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida

PostPosted: Fri Sep 10, 2010 9:13 pm    Post subject: 2 Digit 6 Cell AIC Continuous Loop 2 Examples Reply with quote

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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