Tour de Force by Christianna Brand

It's 1955 and Inspector Cockrill is getting on in years.  Against his better judgment, he is convinced that he needs to have a bit of fun and so allows himself to be pressured into joining one of those tour packages that take a small group of people around European cities, beaches, churches and restaurants that serve strange food and icky alcoholic drinks. (He just wants chips and a beer.) He is cranky and a poor conversationalist and finds his tour group mates--all of whom act way more happy than anyone has a right to be--tedious.  All he wants to do is read his book--a murder mystery, unsurprisingly--in peace.  (But, secretly, he really enjoys watching little dramas play out among the members of the group: one couple's marriage fall apart and not for the first time, two women fall in love--one for the first time and one for the thousandth time, a flamboyant fashion designer's status is far less impressive than he claims, the tour guide's charming Italian accent fades every time he gets bad news from the company he works for...)

Luckily for Cockrill, just a few days in, one of his tour group mates is murdered so he gets to do what he really wants to do, which is investigate a crime. And, as usual for Brand, this murder is both impossible and too possible: our small group is on an island at the seaside and everyone is dozing in the later afternoon sunshine when one claims she has a headache and decides to lay down in her cabin for a while. And then she is found dead, after having been stabbed repeatedly near her cabin door and then (this is the disturbing part) rearranged so that she is laid out on top of a bright red cape on her bed like Snow White in her glass casket. The problem is that all the suspects were in one another's line of sight the whole time, so none of them could possibly have done it. Yet, we also find out that the murder victim wasn't nearly as nice a person as she pretended to be as she got sadistic pleasure from blackmailing people. She had no need of money, she did it simply to yank their chains. And every one  of the suspects has at least one secret they desperately want to keep hidden.  Except for Cockrill, of course...

So how was it managed? As usual, Brand's style is to have Cockrill ask questions and then come up with a hypothesis of how the murder was done by Suspect #1 but then discover one crucial bit of material evidence that doesn't quite fit.  So, he asks more questions and finds Suspect #2 to be the killer, until ANOTHER material clue is found which proves that theory impossible.  And on it goes, through all the suspects, which leaves us with 6 people, all of whom had an excellent motive for killing her, but it being absolutely impossible for any of them to have done it. By this time, the facts and events have been described and redescribed with corrections, edits and deletions that the whole thing is a complete muddle.  Fortunately, Brand supplies a map so we can keep things (and everyone's line of vision) in mind:

The line of windows at the top of the map are cabins that the tour group members use to sleep in.  The murder took place in one of the middle ones. The huts are where people can get towels or change clothes after swimming. "Jasmine Tunnel" is a tunnel completely covered with jasmine vines and flowers--and is the only place where someone could hide completely out of sight of anyone.

NOTE: Cockrill did NOT go swimming but spent the afternoon sitting in a deck chair reading his murder mystery and snorting derisively at the poor plot points. "Nothing like real life," he thinks over and over. As much as he hates the book, he hates it more when the others interupt his reading with their inane comments and questions. You can see him in the upper portion of the map on the left side, next to Louli, a vivacious woman who wears outlandish red wigs and vivid pink lipstick and sparkly orange toenail polish--Cockrill finds her alarming but also strangely sweet and charming--except when she gets self-conscious and turns into a chatterbox.  

The local police have no interest in investigating as they prefer to spend their time inspecting ships coming into port and collecting "tarriffs" (that is, taking fixed percentages of the goods along with hefty bribes). Cockrill is obviously disgusted and laments their lack of Englishness. So he cuts a deal: if he can lead the investigation, he'll identify the culprit. The police (none of whom speak English well) don't understand what he is saying and he tries to explain his plan by comparing his department in Kent to the CID at Scotland Yard. Once they hear the phrase "Scotland Yard" they are ecstatic: they think he's a Scotland Yard detective and are thrilled to be in the company of someone connected to such an esteemed organization. (You can imagine how this makes Cockrill feel if you remember his experiences working with youthful Scotland Yard colleague, Charlesworth, in other novels.) Yet they are itchy to execute someone--anyone--in the town square as, they believe, this will inspire the townsfolk to be lawabiding. So they compromise: Cockrill has three days to solve the murder and if he can't do it, they will grab whomever they want and execute that person at dawn on day 4.  

So with the clock ticking, Cockrill puts his brain to work and...comes up with diddly.  On the eve of day 3, he resorts to drastic measures: he's going to have everyone recreate their actions of the afternoon of the murder (with him adding a secret twist) with the hope that their actions will expose a murderer. I won't spoil the story by revealing the solution--which was completely unexpected by me, at least--but I will say that, at usual, Brand delivers an excellent cast of absurd characters who all desperately try to hold their shit together but ultimately fail. Unsurprisingly, when the dust settles and the culprit is hauled away, they want nothing to do with one another and each heads for home, sadder but wiser.