Let’s clear the clutter from an example and see the principle. On this board with just the 1’s left (candidates – not solutions), we have two columns with just two 1’s left as possibilities. Now, they are aligned on the same two rows. I’ve marked these special 1’s as 1A, 1B and 1C and 1D. Our logic goes – if A is 1 then B and C will not be and this forces D to be 1. But if A is not 1 then B and C must be 1’s. Whatever way round it is any 1 trapped between A and C or B and D, along those rows, can be eliminated.
This introduces us to the idea of Locked Pairs. The 1’s in A and B *lock* C and D into being the opposite. We won’t know which way round the actual solution is until much later after we’ve cracked more of the Sudoku. But a lot of information is carried in the idea that AB and CD influence each other. To re-cap: What ever A and B are they force C and D to be the opposite if you start imagining them having a solution. But either way, there is no room for any other candidates along the alignment of these two sets of pairs.
Going back to our example, let’s fill in the board with all the numbers and overlay the X-Wing. |