***** NOT A TEACHER *****
I did some detective work.
I found on Google this website: Sherlockian.Net: The textual problems of 'The Resident Patient'
1. It appears that the typographical error appeared when the story was first published in a magazine called the Strand.
2. The story was subjected to many revisions. (Please go to that Google result. You will enjoy it.)
3. I checked the "books" section of Google, and all versions correctly spell it "the."
Student or Learner