The Judas Window by John Dickson Carr (writing as Carter Dickson).
One of the five best locked room mysteries, as selected by 14 established mystery authors and critics (All But Impossible!, 1981. ed. E. Hoch).
The Case:...
The bunk’s mattress was soaked wit blood.
The old-fashioned razor was folded shut.
But it had been recently used. It was smeared with blood.
A voice broke the terrible stillness in the stateroom: “The Blind Barber Has Been Here...