A lot of those puzzles fall into a small number of categories:
- Fermi estimation - how many piano tuners in L.A?
- Church problem - gardeners who may have dirt on their forehead, pirates dividing coins - generally, recursive reasoning about other rational actors
- Discrete Measuring - dividing water or gold or whatever given inconveniently sized measuring devices.
Once you master the solution to one category, all the variations in that category are trivial.
"Freezing up" is precisely the problem; you can solve a lot of these puzzles by following your chain of logic to its end instead of abandoning it when it looks difficult or sketchy.
Whether these puzzles are good for hiring is another matter.