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| The purpose of this page is to clarify certain terms scattered about the strategies and put them in one place for easy reference. Specifically Weak and Strong Links, or more accurately, links with weak or strong "inference". They were introduced in the X Cycles strategy but have wide application. |
| The diagram on X-Cycles is very useful for this purpose. Figure 1 marks out a classic X-Wing. X-Wings always contain four numbers arranged in a rectangle such that two opposite sides contain just two remaining candidates of a certain number, in this case 9. Such pairs, sometimes called conjugate pairs are the bed rock of Sudoku strategies. They are also known as bi-location pairs, the "bi-" implying one of X in two cells. In Figure 1 the two pairs are at {B3,B8} and {H3,H8}. From a pair it is possible to draw two separate inferences, called weak and strong:
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 Figure 1: Nice Loop on 9 |
| In other words, a strong link is where: !A => B (if not A, then B) Weak links are the opposite: A => !B (if A, then not B) Back to the diagram. Consider the columns 3 and 8 which are part of the X-Wing and are marked with thin double lines. Because there are more than two 9s in the columns we can't draw a strong inference. We can only draw a weak inference, that is, if one of those 9s is the solution all the other 9s are eliminated. Strong can be Weak So far the rough and ready distinction between Strong and Weak links is to do with how many candidates are in a unit – namely, Strong links are formed when only two are present, while three or more imply a Weak link. However, this is not the case. From a strong link we can infer that if not A, then B From a weak link, we can infer only that if A then not B, C, D according to how many candidates there are in a unit However, the following is also true that for a strong link: if A, then not B So, some Strong links can be reversed to give us a "link with weak inference" - if the occasion calls for it. It is perfectly logical to assert on a unit with two candidates of X both:
In Figure 2 we have an array of 6 candidates on a board. A number of strategies can show that the 6 on H9 can be eliminated. I have coloured some cells using Simple Colouring Rule 2 which link up some pairs on the board - either all of the yellow cells will be 6 or all of the cyan cells will be 6. Since H9 can see C8 (yellow) and H5 (cyan) it cannot be a 6 since it can see cells with both colours. |
To take the Nice Loop example from X-Cycles, we can draw links I have done with blue lines. Our aim is to show that the circled 6 on H9 is eliminated because there are two weak links forming a discontinuity. That is all correct and invokes Nice Rule 3. But take a look at the red link {C4,A5}. It is a Strong Link with Weak Inferemce. It is a Strong Link because there are only two 6s in the box but it we are using it to imply that if A5 is a 6 then C4 is not and if C4 is a 6 then A5 is not. |
 Figure 2: Strong Link with Weak Inference |
