A double homicide brings in Holmes and Watson as they uncover a pair of mathematicians who have been working on solving one of the most unsolvable mathematics equations know to man, P versus MP. When mathematician Tanya is questioned on the murder, she is able to lie and come up with an alibi. Unbeknownst to our dream team of investigators, she solved P versus MP and was able to use it to change the time stamp on the bar footage.
Joan is reunited with a man from her past, the son of the man she killed during surgery. Joey asks Joan for money to open a bar him and his friend are opening. We dive into Joan's past when she reveals how her career as a surgeon ended. When Sherlock gives Joan $22,000 to pay off Joey and help her let go of her guilt, Joan decides to invest in Joey's education not his bar.
In the end, Sherlock and Joan become closer when he asks if he can join her next time she goes to visit the burial site of the man she accidentally killed.