Omission
"Omission" is a term I use to encompass several closely related techniques, all involving removing pencil marks under the right circumstances. It is one of the most common and most powerful techniques, so I recommend you read this page carefully, in order to make sure you understand it.
Some of the other terms I have seen used to describe this technique are: "Intersection", "Pointing, "Blocking", and "Claiming," among others.
The gist of the concept is this: when pencil marks in a row or column are contained inside a single block, pencil marks elsewhere in the block can be removed.
Vague enough for ya? Sorry about that. Sometimes a picture is worth a thousand words:
Focus on the top row only. Look at every "7" in that row. Notice how there are only two of them, and both happen to fall inside the left block? This is convenient, because if we refer back to the basic Sudoku rules, we know every row must contain a 7. We also know that every block may contain only one 7.
Can you see where this is going? If we focus on the row and where its 7 might be, we see that all the possible locations are in that block. Because of this, we have to conclude that the block's 7 is there as well, in one of those two cells along its top.
Logically, we can remove all the other 7s in the block! Cool, huh?
But wait, we are not done… You see, the inverse of this logic is also true. Sometimes, it's the block that makes the rule:
In this sample, the block in the middle has only two possible places for its "3" (along the top). And what do ya know — they are both in the same row! Since the block dictates that one of those two cells is the "3", then the "3" for that row must be in one of those two spots as well. You can remove all the other "3" pencil marks in the top row.
Omissions do not only occur with rows and blocks. They can occur just as easily with columns and blocks.
Omission is a very common occurrence. Unfortunately, it is a bit hard to spot. Again, computer programs like Sudoklue can help by lighting up all the pencil marks of a certain number (CTRL + [number]) if you are having a hard time.
