This is one of the so-called "classic" locked room mysteries, in which an appparently impossible murder takes place. In fact, lead sleuth Dr. Gideon Fell lectures at one point about the myriad locked room crime methods. The actual solution to the murder at hand is so convoluted it made my brain hurt; much more enjoyable is the interplay among the characters.
another old one. i still love it. this is a quirky twist of his locked room mystery fame.