Sherlock and John chase down the latest murders. Sabine tells her old math friend Aidan about a remarkable new theorem. After Jim lets Sabine see where he lives, he drops dark hints of a new plot. Sabine decides it's time to send Sherlock a new code.

In the 1970s, young Jim tries to save his family further trouble.

In the wake of the arsons, Sabine tries to derail Jim's attempt to frame Sherlock Holmes.

Back in the 1970s, young Jim shows Sabine what adults do.

2005: Sabine Moriarty's estranged brother, Jim, uses the 7/7 attacks as an pretext to reconnect. She reluctantly agrees to meet him, hoping that in the years of their separation he has recanted his criminal ways and turned over a new leaf. He hasn't. He has a new project, and wants her help— to be the undoing of Sherlock Holmes.

In the 1970s, young Jim tries to send his sister to a magical land.