Freecell is only a moderate challenge but you can almost always win there.
Having been interested in this in the past, I did a bit of research. Comments here indicate that there is only 1 game in the 32K on Windows that is unsolveable though you can get 2 more using an easter egg. Unfortunately, this proof doesn't list the total number of impossible games.
As for using puzzles to get to sleep - I am very envious.
Cheers - L~R