At this stage in my homebrew sandbox game, the PCs are Lv14, Rogue, Cleric, Wizard and Fighter. They are also filthy rich by the usual standards of D&D, having been sailing around the world in a fast ship, working as successful merchants and doing the occasional Gentleman Adventurer thing by poking their noses into dangerous situations for the thrills. As an example of their wealth, they recently semi-casually dropped 8 million GP on outfitting themselves, their cohorts, and followers with better adventuring equipment.
So, I'm looking for ways to challenge the players with a problem that they can't solve with violence, and preferably not with magic, so I came up with the idea of a murder mystery.
The PCs, as successful merchants, have recently bought themselves a new mansion, and they've invited their wealthy contacts and other members of high society for a 'house-warming' party... but they're actually product-testing the new line of chocolates that they've been researching and developing, hoping to make sales to their home nation's elite citizens and have word-of-mouth help advertise their new product line.
So I came up with the idea of having a mystery where one of the guests is found dead. Since the house will be full of VIPs who are potential customers, the PCs obviously can't just start hitting things. All I have established so far is that the party is a catered evening ball taking place in the PC's mansion in the capitol city of their home nation. The victim is TBD, and could be one of their cohorts or allies, or any other NPC. The time of year is autumn, and the capitol is in a sub-tropical climatic zone.
However, I have a few problems in planning the event:
I want to ensure that the PCs have to investigate personally and not just 'leave it up to the authorities'. The players are up for the idea of a mystery session, but they are also the sort of players who want their characters to have valid hooks to get them involved.
I want to minimise the potential for the magic users (either the PCs or the magic-using cohorts) to simply magic up a solution. No resurrections, truth spells being of minimal usefulness, etcetera.
In essence, I want the PCs to have a reason to do their own old-fashioned investigating, and present the authorities with a solved case.
What techniques can I use to do this?