> Not necessarily, there are clocks that chime on the quarter or half-hour
> as well, but chiming on the hour is standard.

The question was specifically about cuckoo clocks; I've never met a cuckoo clock that did a single cuckoo on the quarter or half-hour. It's annoying enough on the hour. It's not impossible that one exists, of course, and for the purposes of a puzzle design some licence might be applied (though I don't personally believe cuckoos have anything to do with this).