I have the following things for you to consider:
I would think that following up on a guess could work. However, they MUST give you enough information to solve the puzzle. The process of elimination should work sooner or later, but I have no idea how I'd be able to keep track of what I did.
I would recommend that you try easier puzzles until you get the hang of things. To find the easier puzzles, I have been noting the percentage of players that have completed a puzzle while it loads. If it's lower than say 65%, hit "new game" again until you get one with 65% or more finishers on it.
They tend to be the 4x4 puzzles. I've had one 5x5. I've also been reading the forums to pick up helpful tips.