John Taylor (David Mitchell) is a reclusive puzzle maker who publishes puzzle books under the pen name "Ludwig". His identical twin brother, James Taylor, is a successful Detective Chief Inspector in the Cambridge police force. James has gone missing, and his wife Lucy (Anna Maxwell Martin) enlists John's help to solve the mystery. Pretending to be his brother, John infiltrates the local police station to investigate, and becomes inadvertently embroiled in solving other cases.

	"Episode 1"
Puzzle setter John ‘Ludwig’ Taylor’s life of solitude is upended when his identical twin, DCI James Taylor, disappears. Drafted in by his sister-in-law Lucy, John reluctantly assumes his brother's identity as a detective in the Cambridge Police Authority in order to find clues to his brother’s whereabouts. She tells him about how he had changed in recent months. She also shows him a letter of resignation that he sent her with instructions. John discovers that things have changed at work for James and he has a new partner DI Carter. John is tasked with infiltrating the major investigations team, gathering information and solving a completely unconnected murder of a solicitor, Alan Howells, all whilst remaining in character as his brother. A difficult ask for anyone, let alone a reclusive puzzle-setting genius who rarely leaves the house. Can this master of all things cryptic crack his biggest puzzle yet? DS Finch believes that the killers may be involved in organised crime. The building is shared with 2 other companies. John struggles to come to terms with the task. He then uses logic to accuse Sarah Gilmarch of the murder and she breaks down and confesses to killing him after he ended a 6 year affair.
He finally makes it back to the office where he finds James’s notebook. It contains a cipher that needs solving. John decides to investigate further. James’s son Henry finds the letter.

     "Episode 2"
Still posing as his police detective brother, John Taylor gets drawn into the investigation of another man's disappearance during a team-building seminar held in a stately home. Once again, John uses his logical skills to untangle the incident, while James's wife Lucy reminds him he's meant to focus on finding his brother. A bigger mystery behind James's disappearance begins to take form.

	"Episode 3"
The murder of a Cambridge tour guide tests John's logic, while Lucy conducts her own investigation into a case whose details were left by James in an old fax machine and found by John and Lucy in Episode 2.

	"Episode 4"
John Taylor, continuing to impersonate his police detective brother, gets caught up in the investigation of a suspicious death on a building site.

	"Episode 5"
The headmaster of a school is found apparently hanged in his study. John Taylor, a former pupil of a similar school, is convinced it is murder. He attempts to solve the case with the assistance of his former teacher and mentor, who has moved to this school, who also deduces that John is impersonating James. After receiving a strange phone call, Lucy goes on a covert mission to unravel the mystery of James's disappearance.

	"Episode 6"
Holly, the police technology specialist, is found dead in her flat and Lucy is arrested at the scene on suspicion of her murder. Lucy is found with a knife that is later proved to be the murder weapon. Lucy denies killing Holly when questioned by DI Carter, and claims that she had been called by Holly. Lucy tells John in an illicit call that she thinks someone may have been posing as Holly. CC Ziegler demands the matter is resolved quickly. When Carter formally questions John about the nature of his relationship with Holly, he confesses that he has been impersonating his brother James. Holly’s flat reveals that she was conducting her own investigation. The hunt for James takes a back seat as John desperately battles to prove Lucy’s innocence. Angry at James for abandoning his family, John questions whether his brother is worth any of this. Carter fills in Shaw about all they know of James’s disappearance. Evans thinks Holly’s comment about a kiss may have been a test and that she was testing whether he was actually James or not. John thinks that he may well have solved the case. He believes that the killer had barged in before Lucy arrived. The killer hid when Lucy arrived and swapped knives before escaping unseen. Holly’s boyfriend Adam confesses: he is not Holly’s boyfriend but was helping her gather and sell information to those such as Sinclair. James had been taken off the Sinclair case. When he persisted in investigating, Holly planned to blackmail him. She then realised that James was actually John and decided to blackmail Lucy. The documents and files taken from Sinclair’s house never got to Scotland Yard as intended.
Cambridge Police contrive James's resignation. John receives a cryptic phone call from James, leading him to Sinclair’s hidden files. John is re-engaged as a paid consultant to solve crimes.