ID a short story from my vague recollection

About ten years ago I read a book with three (I think) short stories about the same (I think) detective, one of which (the only one I remember) involved the detective guy betting the warden of a prison that he could escape from any cell. He manages to escape by getting a friend on the outside sneak some acid in (I think). Somehow this makes one of the other prisoners break down with remorse for his crime, which was (I think) throwing acid on a woman’s face.

Anyone know what I’m talking about?

American journalist and mystery writer Jacques Futrelle wrote a series of stories with his character Professor Van Dusen, “The Thinking Machine”. The particular story you’re remembering is “The Problem of Cell 13”. I remember reading several of those stories when I was young.

Futrelle was among the lost on the Titanic in 1912.

One of the great mystery stories of all time. Alas, most of Futrelle’s other Van Dusen stories are only so-so. There was a recent collection of them with an introduction by Harlan Ellison, and even Harlan admits the rest of his stuff were mere potboilers.