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Continuous Loops

Points. Continuous Loops are rather simple, made of a closed loop with even numbers of truths and cover links. All truths are bi-valued and can be rows, columns, boxes, and cells. The cover links can be any of the 4 types as well. The most important thing about continuous loops is that they eliminate all extra candidates in the linking cover sets. These loops are often referred to as continuous nice loops. Conventional definitions of nice loops are sometimes overly complex because cells are considered a bit differently from rows, columns, and boxes.


Continuous Loop 1. The example on the right forms a continuous loop of length 4. Two row truths (red), one cell truth (blue) and one small box truth (brown). Like all continuous loops, its truths are linked by an equal number of cover links.


In this example, there is only one extra candidate in one of the cover links, r5c3<>5.



Continuous Loop 2. The second example is a longer loop with 5 truths that eliminates 7 candidates (red).



Continuous Loop 3. This example is interesting because all of the five truths are in rows and because each of the 5 cover links eliminates candidates. The logic diagram for this loop is shown below.





Logic Diagram, Continuous Loop 3. Each row is a truth and each column is a link. Eliminations are in red.



     (4c4)  (3n5)  (6c6)  (8n7)  (8n8)


4R8: 4r8c4=======================4r8c8 

       |                           |   

4R3: 4r3c4==4r3c5                  |   

       |      |                    |   

6R3:   |    6r3c5==6r3c6           |   

       |      |      |             |   

6R8:   |      |    6r8c6==6r8c7    |   

       |      |      |      |      |   

8R8:   |      |      |    8r8c7==8r8c8 

       |      |      |      |      |   

     4r7c4  1r3c5  6r7c6  1r8c7  9r8c8