Which episode ended Sherlock's original UK run on 15 January 2017?

The episode that ended Sherlock’s original UK run on 15 January 2017 was “The Final Problem.”

It is the third episode of series four and the thirteenth episode overall. BBC One broadcast it on 15 January 2017, following “The Six Thatchers” on 1 January and “The Lying Detective” on 8 January.

The episode centres on Eurus Holmes, Sherlock and Mycroft’s previously concealed sister, and her elaborate psychological challenge on Sherrinford. Its title echoes Arthur Conan Doyle’s 1893 story “The Final Problem,” in which Holmes and Professor Moriarty apparently die at Reichenbach Falls.

No further Sherlock episodes had been produced after this broadcast, so the programme’s original run ended with this episode. It is often called the series finale, although the wording “original UK run” leaves room for the possibility of a future revival rather than claiming the franchise can never return.