I've never achieved a monthly trophy, but I had a simple system to achieve record times when I felt so inclined.
Before Logic Puzzles added heavily to their puzzle list, I worked 4x5's exclusively, and soon discovered that the solutions to puzzles containing a '5 person' clue could be predicted solely from the 'x' pattern resulting from that single clue. Of the thousands of 4x5 puzzles, there were probably only about three-hundred patterns, and it seemed like two-thirds of those contained one '5-person' clue. And those '5-person' clues always resulted in nine 'x's. Most of those made for 4 'x's in the uppermost 5x15 squares. I focused on those.
I printed up sheets of blank grids, onto which I would record the four upper deck 'x's from the '5-person' clue of a given puzzle, and then, after solving, I would also record the 15 answer circles. Repeating this until I had around 120 distinct patterns was enough so that I could simply 'look up' the answer to a large percentage of the 4x5's that I encountered. I arranged the patterns in a quasi-numerical order according to where the 'x's fell row/column-wise, so I could quickly locate a particular 'x' pattern/solution that matched a new puzzle, and simply plug in the answers. It was crude, but I achieved some blazingly fast 'solve' times. Several were in the thirty-something seconds range.
My main motivation was to equal, or eclipse, the crazy records I saw. After doing so, I was satisfied that they were achieved by methods essentially the same as mine, and I threw all my cheat sheets away. But it was fun thinking about how it so irked and confounded some players. There you go!
Last edited by bocci; 12-15-2013 at 11:08 AM.