What we are saying when we do this is that either *all *X or *all* Y must be 7.
When we have a pair of candidates we are have two possible logical statements:
Either
X => !Y (If X is 7 then Y is not 7)
Or Y => !X (If Y is 7 then X is not 7)
All we have done with Colouring or Chaining these pairs is extend the length of the statement.
A3 => !A9 => H9 => !J7 => J3
Or !A3 => A9 => !H9 => J7 => !J3
Our chains of X and Y are mutually exclusive possible positions for the number 7 solely because they are formed by pairs. Now how is all this useful? If there is a candidate 7 which is on the chain or even somewhere else on the board that can see both an X and a Y (or two cells with different colours) then that candidate can be eliminated. Another way of looking at this is we’ve proved that either X or Y must be a 7 so there is no possibility that another 7 can exist on any cell that X and Y can both “see”. |