So you three links which are open ended - i.e not joined and forming a loop. D and E are also locked pair being in the same Row and line joining them can be called Link 3. B and D are also locked pair being in the same box and the line joing them can be called as Link 2. (1) A (6,9) and B (6,9) are locked pairs and can call the line joining them as Link I as A and B are in the same Row. But what I felt was you could have explained in simpler manner as under :. You have tried to explain a rather complicated and advanced technique. If we had more nodes we could carry on like this and look for distance 4 paths representing new complementary pairs but distance 4 is not possible in this example. There are only two possible paths in this example, and again they can only be between locked pairs at this distance. These paths represent connections between newly discovered locked pairs. In figure 3, we are mapping all the possible pathways of distance 3. Topologically there cannot be ANY red links matching two locked pairs with What we are mapping here is all the complementary pairs, and I've drawn the links green. Valid pathways must be along the routes defined in Figure 1. Now, in figure 2, we map all the pathways of distance 2. Let us say these links have a distance of 1 between the nodes. I have drawn in red the links between locked pairs and ignored all other links. Arranged in a pentagon as a network diagram each cell has four links to every other cell. We have five cells with the same pairs of numbers. Can we do this logically, or must we guess? What about cell X which also looks like a candidate for removing the 6 and 9?Ĭonsider Figure 1. The point of this test/strategy is that we want to eliminate the 9 from cell Z and leave the 8. On the diagram on the right I have marked all locked pairs with a red line. This forms the basis of Test 3 in my solver. We can therefore eliminate other 6s and 9s from the same row. This means the number 6 and the number 9 MUST both occur in these two cells. For example, in the diagram on the right in the top row: 6 and 9 occur twice (labelled A and B) as a pair on the same row. A locked pair is two such cells which lock each other in. Pairs occur where two or more cells have the same two possible numbers. Since first writing about it the strategy has been expanded in several directions and is more common than first thought. I coined Remote Pairs (back in 2005) to distinguish this strategy/test/check, whatever, from the simpler more obvious pairs.
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