One of my favourites is an old wooden puzzle I found at a second-hand store many years ago. Even when I bought it, I knew it was missing a couple of pieces. I didn't care.
There's something about the way the thick pieces click into place that is much more satisfying than the non-sound that comes from putting cardboard pieces together.
I suppose if I get desperate, I can open one of my precious Beatles' puzzles -- ones I've kept sealed in case they ever get valuable... this one, which is not only of my favourite of their films, but might well be what I'm asking for: Help!