I am a cheater. I do have a guide to the Professor Layton puzzles, and I'm not ashamed to resort to it. I do use in-game hints, but if the in-game hint seems to be way behind the level of thinking I've gotten to, I tend to suspect I've either GOT the answer but made a mistake in calculations or that I'm missing something so obvious that no hint will point it out. One or two puzzles I don't think are entirely fair but this way I'm not bogged down long enough to get annoyed at it. If I'm not making progress, I'm willing to cheat to move on. If I'm getting there, I'll keep poking at it.
... Slider puzzles, I hate. I'm not going to sit and fool with pieces of a picture being slid around.