What are the key elements of the setting in Futrelle's "The Problem of Cell 13," aside from the fact that he is in a prison cell?

The first part of the setting of "The Problem of Cell 13"
of course is Van Dusens's home. One may imagine his laboratory where he proves "that two
and two always equal four, except in unusual cases, where they equal three or five, as
the case may be" and that "all things that start must go somewhere." However there is
nothing in the text to support the image of the first part of the story being set in his
laboratory. Part of the setting includes the era of the story; Jacques Futrelle wrote
"The Problem" is 1905 and it is set in 1905.

Once the story
shifts to the prison, we know that the setting is Chisholm Prison. Chisholm is in
Beaufort County in South Carolina in the U.S.  The setting at Chisholm begins where the
three men--Ransome, Fielding, and Van Dusen--are greeted somewhere in the prison by the
warden. The setting then accommodates a place to search Van Dusen. One may imagine the
warden's office for these steps but, again, there is nothing in the text to identify the
specific location of the greeting or the search. We do know that the next shift in
setting includes jailers--who are not part of the setting--who will allow no
communication from Cell13 and will report anything Van Dusen says or hands over to
them:

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Absolutely impossible [to communicate]. ... Not
one word, directly or indirectly. ... They will report anything he might say or turn
over to me anything he might give
them.

The first actual
description of setting comes when the warden escorts them to Cell 13. We are told the
warden  "led [them] back into the prison ... stopping three doors down the steel
corridor," and that the warden then said, "It's only three doors back of my office." And
we know there is a "heavy steel door" with double locks. We also know the setting is
bestrewn with scurrying rats: "dozens of them."

Finally,
once Van Dusen is tucked away and quietly thinking, we are given some broader
understanding of the setting. Chisholm Prison--large, four stories, and made of
granite--is surrounded on all sides by open space and bounded by a "wall of solid
masonry eighteen feet high." The prison is completely isolated--there are no signs of
civilization near it at all, just "acres of open space." We are also told that a river
lay beyond the wall nearest to Cell 13: Van Dusen knew this because of the sound of a
motor boat and the presence of a river bird in the air. Further, he discerned that
between the river and the wall was a playground where children were playing baseball:
"came the shouts of boys at play and the occasional crack of a batted ball." These
details ofsetting and a few others regarding paint and an outmoded pipe system were
later confirmed by one of the jailers.

Other essential
aspects of the setting are that his window was only three to four feet above the ground
and there were seven doors to pass before getting out of the prison: "seven doors to be
overcome before one could pass from Cell 13 into the outer world, a free man." In
addition, though there was an opening of about two inches below the heavy steel door,
the rats, when frightened, got out of the cell some way other than under the door--there
was another egress in the cell, no matter how small.