copyright (c) 2010, 2014 by R. Rodman
The following are the techniques I use to solve Sudoku puzzles. There are basically 4 techniques. The first two are usually sufficient for easy to medium puzzles. Generally I do the Crossing Patterns first, 1 to 9, then the Missing Number, then other techniques as required.
Crossing Patterns: (aka Beams) Here you imagine vertical and horizontal beams from each 1, looking for cases where there is only one square left for a 1. You can also notice places where a 1 goes across, and there are two or three places in a single row in a far square, so you can imagine another beam coming from there. It's a little hard to describe. A figure could help. I'll come up with one later. After you finish the crossing patterns with 1, you then do 2, and so on. By the time you get to 9, many easy puzzles will be finished.
Missing Number:Here you go down a row, column or box and look for each digit. For example, if you don't have a 1, look at each empty square and ask if it can be a 1. If there is only one possible place for the 1, fill it in. After doing 1, do 2, and so on. Do rows, columns or boxes missing only 2 or 3 digits first (if they're missing only one, you can figure out what it is and fill it in). Alternate going horizontal and vertical for best results.
Only possibility:In this case, you pick one empty cell. Look for a 1 which impinges on it, then a 2, and so on. If there is only one possibility, fill in the cell. This technique works if there are lots of filled in cells at right angles or in the same box as the empty cell.
Squeeze play: can be used if you have a Notes feature. Using the Missing Number technique you can label the cells with the numbers that are possible for each cell. You will often find that there are two cells with a pair of numbers that cannot be anywhere else in a 9x9 box, for example, these two cells must both be 3 or 5. Knowing this, no other numbers can be in those boxes. Often a 9x9 box will have two such pairs, blocking out a lot of its space, forcing remaining numbers to be in the remaining squares. Squeeze plays can also be used on rows or columns.
Shot in the Dark:This is a desperation move. In a very difficult puzzle, you will often come up with the case that every empty cell has more than one possibility. So, you pick a pivotal cell with only two possibilities, pick one; write it small in one corner of the cell; then work through the rest of the puzzle with small numbers. There are three possible results: A contradiction, in which case the shot was wrong; completing the puzzle, which means the shot was right; or an inconclusive result, which means you didn't choose a really pivotal cell, so erase the little numbers and pick a different one.
If anyone's interested I'll add figures to support this article. If not, I won't. Have fun!
Rick Rodman, originally 8/16/2010, revised 12/3/14.