In this room the correct door has “hem” in the dark. The folded up cloth that has been sew has been hemmed.

> Ducking behind a curtain and hurrying down a passageway we came out in

There’s hem/hemming in the way. It’s referencing Hemingway.
The mention of “duck” in the sentence they use with “way” means to use his book about duck hunting: “Across the River and into the Trees”.
In room 24, the abyss, we are told it’s Stygian gloom, so the river is the Styx.
Across the river Styx = Acrostics.
The full quote the book title is based on is is: “Let us cross over the river and rest under the shade of the trees.”.

“Across the sticks and in-two the shade of trees” is describing the wooden chair shadow. It is an X then / then /. Or a strike and 2 spares since theres a bowling pin. This same pattern of “X then wooden / / shadow ” happens in room 23. I havent solved it yet.
——-
.2.
Theres an equals sign on the left chair. The equation is:
FACE-(HEAT-HAT) = FAC
Which gives you door 13 as the notes are F:AC.

I did ctrl+F for HEAT and nobody had this. You need to subtract HAT (in many rooms) because its on sacrificial tripod in room 15. The text about “SUMone lost his hat” and “are you sure its the hat that is lost” is about how technically you are adding the HAT in that above equation as its negative negative.

We know to subtract because if you draw a line from the FACE to the F it goes through ACE. This shows the straight line subtraction principle.

———
.3.
Theres an ACE on the wall. wall-ace. William Wallace was a true scotsman, so this is the opposite of No True Scotsman fallacy. The correct door is closest to the wall-ace.
Some other logical fallacies in the house that denote traps: Red Herring, Slippery Slope, Black+White, Easter Island head, Gamblers.
——–

Notes:

- HAT gets removed because of the hat on sacrifical tripod in room 15.

- FACE is used in chemical symbols (CUP/MUG/FACE/CAFE) answers in room 1 and 5. FACE cant be spelled in chemical elements but FAC can. So again in this room only the correct door can be spelled using chemical symbols in puzzles using “FACE” in some way.

- The ACE looks like a pen nib. Above it is “…”. And we have “across” hinting about acrostics. So read the letters below “…” in the text. You get “the eno D we”. This anagrams to “hewed note” or “hew denote”. This is a useful phrase for figuring out “hem” in this room and “hew” in room 5 (another FACE room).

In any case shadws play an important role in the picture for sure. The shadow of the chair… does it make some kind of cross pointing to 3?

I have always liked to think of the fireplace as an opera singer. Casting music in the form of light. Like if you could get lost in both fire and music.