The Unicorn Murders

Classical impossible crime / locked room mystery by the master of the genre.

Kenwood Blake is with the British Secret Service and romantically
involved with another agent, Evelyn Cheyne. Together with Sir Henry
Merrivale, they become embroiled in a battle between Flamande, the most
picturesque criminal in France, and his arch-enemy Gaston Gasquet of the
Sûreté.

Both Flamande and Gasquet are masters of disguise, and no one
knows what either man looks like. Blake, Merrivale and an assorted
group of strangers are in an airplane that is forced to land near the
Château de l'Ile, where the Comte d'Andrieu is apparently expecting
visitors and offers them all his hospitality.

One of the plane's passengers falls to the ground with a hole in
his forehead, as if he had been gored by a unicorn, and the area where
he fell was under observation by impartial witnesses such that it seems
impossible for anyone to have committed the murder.

Sir Henry must sort out the twin problems of who's really who and whodunnit.