I'm finding that some problems are easily solved using abductive reasoning which most players fail to apply. It's not a matter of finding the right plan. It's a matter of finding a series of one-mover "only" moves. Take 0044966 for example (hints available below the puzzle once you click "show solution" or "FEN/PGN" - I added these hints but the don't appear in puzzle mode):
I suspect the reason for this is because Tactics Trainer is incapable of handling problems with multiple solutions. Since there's a finite number of interesting problems which have only one solution, there are two options:
1. Add simple, uninteresting problems such as the one above to the database to increate the number of problems, so members will not see the same problems multiple times.
2. Enhance Tactics Trailer to handle interesting problems with multiple solutions. Which Chess.com did, but they branded it Chess Mentor and limited it to paying members instead of releasing it for free to attract new membership.