
Forbidding Chains 

A Forbidding Chain is a chain of a single value of candidates, with alternating weak and strong links. If the chain returns to the first point, and the first and last links are both weak, then the starting/ending candidate can be eliminated.
A strong link is two candidates that share a unit in which they are the only candidates. A weak link is any two candidates that share a unit, regardless of whether or not there are others. Thus, a strong link is also a weak link, but a weak link is not always a strong link.
In a forbidding chain, more than one candidate can be a node in a link, as long as they all share a unit with the next node.
Remember again that Forbidding Chains only consider one value.
Consider the example on this page. A Forbidding Chain of 3's is highlighted in orange. Remember that a forbidding chain must begin and end with a weak link. Starting with the 3 in blue, it is weakly linked to the 3 directly to the right, which is strongly linked to the 3 directly above, which is weakly linked to the 3's in the same box, which are collectively strongly linked to the 3 on the far right, which is weakly linked to the 3 directly above, which is strongly linked to the 3 on the far left, which is weakly linked to the original 3 in blue. Thus, the 3 in blue can be eliminated.
Consider the following logic. If the 3 directly to the right of the blue one is false, then following the links you see that the upperleft 3 must be true. Thus, whether the 3 to the right of the blue one is true or false, the one in blue can be eliminated.
Sudoku Snake gives Forbidding Chains a skill value of 1100.






