It is possible.
I can regularly solve these puzzles pretty quickly. While my average time is something like 170 seconds, I have solved 4x4 puzzles on this site in as few as 65 seconds. No cheating, no pattern-memorization; I just solve them using logic, and using the geometry of the grid, which is, after all, why it's there. Here's how I do it:
Reading the clues is the slowest part of the process. First I fill in the grid with the *solid* facts as quickly as I can. X's and dots. Then there are usually 3 sometimes 4 clues which are not direct dots or exes, but rather relational information between categories. These three I memorize as I skip past them and then fill them in last. From there (and with those 3 sometimes 4 clues in my head) I focus on the grid. All the information is there. No more reading: rereading clues is what slows you down, and once the info is on the grid you don't need to revisit the clues. I do use geometry: if there are 3 dots on the grid forming a partial rectangle, I know to fill in the last dot.
I also save time by skipping extraneous X's. No need to fill them all in, if you can look at a grid of dots and learn to see where the X's should go without having to laboriously click click click them all in place. If I can see in my head that two lines of X's "added together" leave a single gap between them and I know they are equivalent, I know that gap has to have a dot without clicking in all the exes to prove it.
Also sometimes when I get the puzzle down to only 2 dots missing, I guess, and if it's wrong, I go back and switch them. While I could use the clues to solve it, guessing the last two dots -- even if I get them wrong the first time -- can be quicker than trying to find the relevant clue.
Maybe the problem is that all these puzzles are structurally so very similar. That doesn't mean it's cheating to learn how to do them quickly. Some greater variation in their construction might be a good idea.
Last edited by DumperDimple; 04-02-2013 at 09:15 PM.