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Almost 2 digit 6 cell AIC Continuous Loop/ AHP 2 Examples

 
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Bud



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

PostPosted: Fri Oct 08, 2010 1:33 am    Post subject: Almost 2 digit 6 cell AIC Continuous Loop/ AHP 2 Examples Reply with quote

In my last post I gave 2 examples of a 2 digit 6 cell AIC continuous loop. In this example a third form of this type of continuous loop is almost present in the *marked cells except that there is an extra 1 in r9c9. Note that without this 1, the pattern would be a 9 4-cell AIC and a 1 4-cell AIC with the ends connected. Also note that the r89c9 cells cnotain an AHP(19) which is a HP except for the 1 in r9c3. If r9c3<>1, the AHP r89c9 = 19 and r8c9<>34. If r9c3 = 1, then r9c9<>1 and the almost continuous loop is true and r8c9<>34.

Almost Continuous Loop/AHP Example #1
Code:

+----------------------+------------+------------------------+
| 1479   14679  146    | 46  5   3  | 467    2        8      |
| 234    348    234568 | 9   17  17 | 3456   346      345    |
| 3457   3467   3456   | 46  2   8  | 9      13467    13457  |
+----------------------+------------+------------------------+
| 3459   3489   7      | 25  19  14 | 2348   3489     6      |
| 149*   2      14*    | 8   3   6  | 47     5        479*   |
| 6      3489   3458   | 25  79  47 | 1      3489     2349   |
+----------------------+------------+------------------------+
| 2347   3467   9      | 1   8   5  | 23467  3467     2347   |
| 127    167    126    | 3   4   9  | 25678  1678     157    |
| 8      5      134*   | 7   6   2  | 34     19-3-4*  1934*  |
+----------------------+------------+------------------------+


After making this move, the puzzle is as shown below. Note that an identical almost 79 contimuous loop and AHP pattern appears in rows 1 and 5 with cells marked by *. Here the additional 7 digit is in r1c1 and the (79)AHP is in r1c12. Again whether the AHP or the ACL is true, 146 can be eliminated in r1c2.

Almost Continuous Loop/AHP Example #2
Code:

+----------------------+------------+------------------------+
| 1479* -1-4-679* 146  | 46  5   3  | 467*   2        8      |
| 234    348    234568 | 9   17  17 | 3456   346      345    |
| 3457   3467   3456   | 46  2   8  | 9      13467    13457  |
+----------------------+------------+------------------------+
| 3459   3489   7      | 25  19  14 | 2348   3489     6      |
| 149*   2      14     | 8   3   6  | 47*    5        479*   |
| 6      3489   3458   | 25  79  47 | 1      3489     2349   |
+----------------------+------------+------------------------+
| 2347   3467   9      | 1   8   5  | 23467  3467     2347   |
| 127    167    126    | 3   4   9  | 25678  1678     157    |
| 8      5      134*   | 7   6   2  | 34     19       1934*  |
+----------------------+------------+------------------------+


The original puzzle is the 10-7-10 Tough at Sudoku.com.au

EDIT: Corrected typos and added Example2.


Last edited by Bud on Fri Oct 08, 2010 1:11 pm; edited 2 times in total
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Oct 08, 2010 6:01 am    Post subject: Reply with quote

For those who might prefer an alternative:

Code:
 (9)r9c8 = (9)r9c9 - (9=471)r5c793 - (1=34)r9c37  =>  r9c8<>34
 +--------------------------------------------------------------------------------+
 |  1479    14679   146     |  46      5       3       |  467     2       8       |
 |  234     348     234568  |  9       17      17      |  3456    346     345     |
 |  3457    3467    3456    |  46      2       8       |  9       13467   13457   |
 |--------------------------+--------------------------+--------------------------|
 |  3459    3489    7       |  25      19      14      |  2348    3489    6       |
 |  149     2      d14      |  8       3       6       | c47      5      c479     |
 |  6       3489    3458    |  25      79      47      |  1       3489    2349    |
 |--------------------------+--------------------------+--------------------------|
 |  2347    3467    9       |  1       8       5       |  23467   3467    2347    |
 |  127     167     126     |  3       4       9       |  25678   1678    157     |
 |  8       5      e134     |  7       6       2       | e34     a1349   b1349    |
 +--------------------------------------------------------------------------------+
 # 124 eliminations remain

-OR-

Code:
(9)r1c2 = (9)r1c1 - (9=147)r5c137 - (7=146)r1c347  =>  r1c2<>146

... and r8c2=1 plus r9c89<>34 follow from basics.
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