In those terms, I hate puzzles and love problems. Puzzles are contrived by humans and are generally as much psychology problems as anything else. They basically require you to think like the human who created them, and they have bizarre and arbitrary constraints that are totally unlike the real world, where, as Feyrabend told us, "Anything goes."

Puzzle-style interviews are 99.9% human made, and one of the features of human-made puzzles is: the answer is known and very nearly unique. This makes them almost completely unlike the real problems programmers encounter, where there is no known answer (if there was, the programmer would find it on Stackoverflow or similar) and amongst the potential answers there is no obvious winner.

So it's really easy to be good at puzzles and terrible at problems, which require taste and good judgment to navigate through the combinatoric explosion of approaches and parameters (and no, design-of-experiments won't do more than give you a little assist on genuinely hard problems.) Problems also require one to know when to stop, when a solution is "good enough" for the given domain. Even problems that are nominally non-statistical in nature require decent statistical knowledge to evaluate potential solutions.

So as someone who designed algorithms for a living for quite a long time, and still does for fun and profit now and then, I'm as strongly against puzzles as the OP. I'm actually slightly biased against people who love puzzles because it looks to me like they are spending way too much time playing with nice, neat pebbles on the beach, when the ocean of ugly, intractable problems lays unexamined before them.