With the help of a mathematician (Rich Sommer) to decipher a complex formula on P versus NP, Sherlock Holmes (Jonny Lee Miller) and Watson (Lucy Liu) investigate the murder of two mathematicians who were working together to solve an unsolvable mathematical problem which could be worth more than $1,000,000 (not to mention incredibly lucrative and massive real world implications) to the person, or persons, who solved it.
In the course of the investigation Holmes and Watson talk with the head a of a security firm (Glenn Fitzgerald) who was secretly surveilling both men as well as another mathematician (Lynn Collins) who lied about knowing about the men's work, both of whom had motive for killing the men and stealing their work. When the mathematician comes up with an apparent unshakable alibi, Holmes begins to suspect her incredulous ex-boyfriend (Richard Holmes) may be framing her for the crime, but the truth is far more complicated.
In the episode's B-story Watson considers loaning money to the son (Jeremy Jordan) of the former doctor's final patient whom she lost on the operating table. Although Holmes agrees to give that amount and more to Watson, he cautions her against giving the young man the money and ending the relationship of as quickly, and permanently, as possible. After helping Sherlock solve the case, Watson comes up with her own solution to the problem. The episode ends on a nice note as Holmes offers compassion and support to his partner's still raw wound that changed the course of her life and brought her to his doorstep.
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