Is it correct to write "the adjacent room" even if there are multiple adjacent rooms?

One matter hasn't been addressed so far: the text the OP discusses is a puzzle. If you're listening to someone telling a story, and they said "I was lecturing once when I heard a strange noise from the adjacent classroom" (an example by the OP), then you might not trouble to ask them to clarify whether it was the one on the left, the right, or wherever. You might take it for granted that this detail doesn't matter to your appreciation of their story.

By contrast, a puzzle is different. The setter (the person posing the puzzle) needs to make it clear what information the solver is told, and what they are not told. Are the hallways connected in pairs but the pairs separate? Or is each hallway connected to both its neighbours? Or perhaps the setter specifically intends not to tell the solver. The solver can't glean this from context, because the puzzle statement is the entire context. In such a situation, accuracy of wording is critical.