__Pairs__

We can make some interesting deductions about the possible contents of a square by looking at pairs of possible numbers contained in other positions in the same row, column, or 3x3 block. Let's have a look at the row below:

__Triplets and beyond__

The same principle applies to triplets: If you can find unsolved squares in a row (or column, or box) which contain the same three possible numbers, then you can be certain that whatever the actual solution may be, those three numbers occur only within those squares - and thus can be eliminated from consideration anywhere else within this row (or column, or box). To make this a little more concrete, look at the following row:

This principle can be extended from pairs and triplets up to groups of four, five - theoretically up to eight. As the number increases, however, the situation becomes not only progressively more unlikely, but harder and harder for the human eye to spot. Pairs will be constantly helpful to you, triplets sometimes helpful, and as for the rest - well, it *might* happen...

__One last complication__

So far we've been talking about triplets of squares which all contain the same three possible numbers. It's actually a bit more complicated than that: Within a row (or column, or box), if three squares contain only three numbers between them - with no requirement that all three of those numbers occur in each square - then any other occurences of those numbers in other squares in that row (or column, or box) can be eliminated. That's a horrible sentence to be forced to read, I know, but things should be clearer after a look at the following:

The most general case of this rule is: if n squares in a row, column, or block contain only a given group of n numbers between them, when n can be between 2 and 8, then any other occurences of those n numbers elsewhere in the same row, column, or block can be eliminated. That's a bit of a mouthful, but I hope we've lead up to it in sufficiently reasonable steps.

What do you do if you've tried every technique there is and you can't go on? Giving up and having a nice cup of tea is probably the best thing, but if you don't want to do that, you could read Tutorial 5.