Because there are only two possible states for a candidate, all candidates with the same color must simultaneously be the solution or can not be the solution. This strategy analyzes such chains and uses colors to display these states (hence its name). If we consider a longer Chain exclusively made of Strong Links, the successive Nodes alternate from one state to the other. This, in turn and for the same reason, implies that the candidate can not be the solution for the third Cell in the Chain.Ĭonversely if we assume that the candidate in the Cell at one end of the Chain is the solution for that Cell, then it can not be the solution for the middle Cell and it must be the solution in the other end Cell of the Chain. If we assume that the candidate in the Cell at one end of the Chain is not the solution for that Cell, then it must be the solution for the next Cell in the Chain because of the definition of a Strong Link. If two Strong Links share a common Cell, we can form a Chain of three Cells with the common Cell in the middle. Let us define a Strong Link as the relationship that exists between two Cells in a region (Row, Column or Square) when these two Cells are the only Cells in that region that contain a particular candidate: if the candidate is not the solution for the first Cell, it must be the solution for the second Cell, and vice-versa.