by Robert Benson
(San Diego, CA, USA)
While I use all the methods you give, one of my favorites (which I have not seen in print yet) is to use “coupled pairs” of numbers. The major drawback of this method is that not all puzzles are suitable for this. When it does appear, though, usually it is extremely useful.
In a 3×3 grid (a “square” in my terms) many times you will be able to identify an individual “cell” which has only two possible values (e.g., 4 and 7). The coupled pair is when in the same square you can identify ONE OTHER cell that has the same pairing (another 4 and 7). That is to say, in the square the same two numbers can ONLY appear in those TWO cells. I write these two numbers in small type in both upper left corners and circle them.
The implications are obvious. Now you know where those two values go (although not which is which yet), so you can look at the other empty cells in the square and eliminate those numbers from them, as well as eliminate the other numbers from the coupled pair.
The tricky part is identifying coupled cells, because sometimes a coupled pair is hidden. That is, there could be multiple numbers that appear as a possibility in the cells (e.g., 4, 5, & 7 in one cell with 4, 6, 7, & 8 in another cell). However, when you see that 4 & 7 can ONLY appear in those TWO cells, the other numbers (5, 6, & 8 in this case) can be ignored; those two cells exclusively sharing 4 & 7 form a “coupled pairing” of cells.