I've seen TV show episodes that use the terms "scavenger hunt", "treasure hunt", "mystery hunt", and even "ARG" in reference to the type of entertainment known as "pervasive games". However, I had never heard any of them use the phrase "puzzle hunt", even when referring to something that I would consider to be one.
That changed a few nights ago when I watched a new episode of "Elementary", the Sherlock Holmes-in-America CBS show.
In it, an overly-obsessed math genius is participating in what he calls a "puzzle hunt" with a cash prize. The puzzle hunt in this case consists of solving a math problem that yields GPS coordinates, finding a phone number at the location, and then calling the number to get access to the next math problem. Does this qualify as a puzzle hunt, though?
I've tried before to nail down a concise definition of what a puzzle hunt is, but my attempts have been found to either be too narrow, or so broad that making a telephone call would qualify. In general, I find that the solve puzzle to unlock location of next clue / repeat until end of hunt works for me. "Puzzle" is the vague part in this series: Does a riddle qualify? Do math problems (regardless of whether they use palindromic primes)? Jigsaws? Entanglements?
All of these, to one degree or another, meet the requirement of testing the solver's ingenuity to solve the problem. That makes them puzzles.
However, if a hunt consists of all riddles, I don't think of it as a puzzle hunt, but a riddle hunt. In other words, when a hunt is limited to only a specific type of puzzle, then a better label is "[puzzle type] hunt". A variety of problem types would necessitate "puzzle" as being the best catch-all term. What was shown in "Elementary" would be a "math hunt"… though honestly it sounded more like a math-based geocaching ARG.
A so-far attempted writer myself, I've had occasion thoughts on how to construct story about a murder in a puzzle hunt setting. None of my ideas, though, have inspired me to commit pen to paper (or fingers to keyboard). It seems that the longer a mystery show is on, the more likely it will contain a hunt, whether it be scavenger, treasure, puzzle, or ARG. Some are entertaining, but none to date have truly satisfied what I think of a puzzle hunt. Even this episode, which specifically called its McGuffin a puzzle hunt, fell short.