The case in question is Remote Island Syndrome
Part 1 and 2
I was a reluctant The Melancholy of Haruhi Suzumiya watcher a bit after the hype had subsided slightly. These two episodes are what made me like the show enough to remember it fondly. These episodes contain classic murder mystery tropes as well as a bit of character growth on the part of Haruhi.
It is interesting to look back on the Melancholy of Haruhi Suzumiya if for nothing else to remember what a phenomenon the show was when it came out in 2006. It seemed like Haruhi was everywhere then. You could not go to an anime convention and not see someone doing the Hare Hare Yukai dance all day and it dominated the discussion of anime in general. While Haruhi Suzumiya has hardly disappeared from the otaku consciousness its presence was greatly diminished by the infamous Endless Eight. So it is nice to look back on the mystery in one of the more iconic episodes of the series and recapture a bit of the magic of the first season.
The gang travel to a mysterious island which they were invited to by a one of Kozumi’s acquaintances. Once there, a storm rolls in cutting them off from the mainland. And there is a locked room murder. Sound familiar? Whether through unlucky circumstance or the wishes of Haruhi for just such an occurrence, they must solve the case.
Itsuki and Kyon start the episode being a bit worried that the island they are to is going to be a major problem with an adventure craving unknowing goddess like Haruhi. Since she seems to be in the mood for a mystery a small private island would be the classic place for a closed-circle murder mystery to take place. Sure enough while everything seems to go well eventually a storm conveniently rolls in and the worst case scenario occurs.