Interviewers ask puzzles and give you tricks because they want to see your problem solving process. Obviously, anyone who hires simply off a litmus test of such questions is not doing their job, but that doesn't preclude the use of such brain teasers/problems at all. Asking a candidate a difficult brainteaser that may be even close to impossible can be extremely revealing. There isn't a canned response, you get to se…
I prefer problems that are ridiculously simple on the outside; however, allow for lots of optimization. Choose the next best move in chess or go for example (or design a simple sudoku solver). A completely simplistic solver just chooses a valid move. It becomes more interesting as one looks at how are you modeling state, how are you deciding what is best, etc. This way most people will get something that works, you can see their thought processes (where are they optimizing first, why are they doing that), and maybe learn something new.