Find Naked and Hidden Singles and Pairs First
(Auburn, MA, USA)
After first pass through clues
Yes, everyone says to do that, but no one explains how to do it systematically. Here is how I do it:
I first create a frequency distribution of all the clue numbers in the grid. Like this:
4|3 2 5
3|1 8 9
I then start with the most numerous clues. 4 and 6 both appear 5 times in the puzzle so I start with those.
I will do two passes through the clues. On my first pass naked singles are easily spotted using the "scan" technique. I will write in candidates, but only if there are only two candidates in a row, column or block. This makes it easy to identify hidden pairs on the first pass through the clue numbers. When a cell is solved, I check to see if any of the prior clue numbers are in scope of the newly solved cell. If not, the solution has eliminated a candidate for that clue and I recheck it. If all candidates are entered for a clue during this pass, I put a slash through that clue as a reminder that I don't need to check for candidates for that clue again.
I write my candidates around the inside edge starting with 1 in the upper right corner. 3 upper left, 5 lower left, 7 and 8 sharing the lower right, and the others filling in along the walls.
When I find a naked pair, as a reminder I lightly draw a rounded square in each cell to prevent other candidates from being written into the cells. I've lately extended this to drawing a faint line or corner in the cells where candidates have been eliminated by the existence of other candidates in a row, column or block; again, just as a reminder that they have been eliminated so I won't be tempted to write in those candidates if I have to put the puzzle down and return to it later on.
After the first pass through the clues, I then look for blocks, rows and columns with only two unsolved cells in them and write in the candidates. In many cases the solutions to those cells reveal themselves easily. Repeat for triples, quadruples and quintuples.
Then make a second pass through the clues, writing in the remaining candidates and seeing if solutions or eliminations can be done via color chains.
After all the candidates are written in, look for hidden triples, x-wings, xy-wings and xyz-wings. Once those are found, only the extreme puzzles will not be solved by this point. If it's still not solved, break out the Gordonian rectangles and polygons, xy-chains and the rest of the extreme techniques.