"The Napoli Express", by Randall Garrett

The Napoli Express makes the run from Paris to Naples only twice a week. In the first-class cabin there are eight cabins, with room for sixteen passengers total, though on this run one of the cabins has only a single occupant. Two of the passengers on board for this trip are Lord Darcy, chief criminal investigator for the Duke of Normandy, and his assistant, master sorcerer Sean O Lochlainn, both with suitable aliases.

As the train makes its way down through Lyon to Marseille on the Mediterranean coast, and then along the coast to the duchies of Italy. Very late during the second night of the journey, Sean and Darcy hear the other occupants trooping along the corridor, one at a time, to the compartment containing only a single traveler, a man named John Peabody.

In the morning, Peabody is found dead, bludgeoned to death. A dozen blows to the head; a dozen visitors in the night. Coincidence?

Randall Garrett's Lord Darcy stories are set in an alternate history where English King Richard II did not die of a crossbow wound, but lived to found a Plantagenet dynasty that survived to modern times, and in which magic has been codified and is used in place of science in our own. Despite this, they are fair-play detective stories in which a rational solution can always be found - no magic required.

Garrett was also fond of seeking inspiration from the classics of the mystery genre. The most famous instance was his novel Too Many Magicians, in which a main character resembled Nero Wolfe and has a smart-aleck assistant named Bontriomphe ("good win"). The title of that one is quite similar those of Rex Stout's novels Too Many Cooks, Too Many Women, and Too Many Men.

In this case, of course, he's taking on Agatha Christie's Murder on the Orient Express. His solution is ingenious, and he even slips in some subtle criticism of the original.

You really can't go wrong with the Lord Darcy tales, which are available in a collection simply called Lord Darcy, which is out of print but easily found.