Getting Happy with Parker Pyne: The Gate of Baghdad by Agatha Christie

Parker Pyne is still abroad, spreading his statistician-acquired
cynical know-how the same way his forebears spread smallpox, this
time on a "Pullman coach" across the desert from Damascus to
Baghdad in which a sock may or may not have been used to murder
someone. Where's Rob Kardashian when you need him? Fortunately,
he's right here!