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Continuous Loops with ALS

Points. ALS and AHS can take the place of ordinary truths in many types of logic, including rank 0 continuous loops.


Continuous loop with ALS. The example on the right forms a continuous loop of 3 cells and one 3-cell ALS. The 6 cells (truths) are linked by 6 cover links. Continuous loops eliminate all extra candidates in any of its cover links, thus the 5 red candidates for digits 3, 5, 7, and 9 are eliminated.



Continuous loop with ALS 2. This example is similar to the above except one of the truths in the chain is a row in row 3. Like all continuous loops, its 5 truths are all linked by 5 cover links, eliminating the red candidates 1, 4, and 7.





3D View. The ALS is made of the 3 interconnected blue cell truths on the right side of the loop.


Logic Diagram. Example 2. Each row is a truth and each column is a link. Eliminations are in red.


     (7r9)  (4b9)  (1b9)  (6c7)  (6c2)


     7r9c3  4r8c9  1r7c8               

       |      |      |                 

9N8: 7r9c8==4r9c8==1r9c8               

       |      |      |                 

8N7:   |    4r8c7==1r8c7==6r8c7        

       |             |      |          

7N7:   |           1r7c7==6r7c7        

       |                    |          

6R3:   |                  6r3c7==6r3c2 

       |                           |   

9N2: 7r9c2=======================6r9c2