The Prisoner/Recap/E05 The Schizoid Man

Quoting Wikipedia:

Number Six is assisting Number Twenty-four ("Alison"), a telepathic young woman, in practising mind reading with Zener cards. In an extremely complex plot of bluff and double bluff, Number Two brings an agent who looks just like Number Six, and is referred to as "Number Twelve", to The Village. Number Twelve is also played by McGoohan, apart from some shots featuring a body double.

The real Number Six is subjected to an intensive course of aversion therapy, altering his tastes and instincts, and training him to do everything left-handed. He is drugged to wipe his memory of the treatment. When he awakes, he is treated as "Number Twelve", while the lookalike assumes the role of Number Six. The real Number Six is informed by Number Two of the plan to break "Number Six" (the impostor) by convincing him that he is not Number Six at all.

Six and Twelve engage in various challenges to prove which is the real Number Six; the aversion therapy allows the impostor to behave more like Number Six than the real Number Six does. In the presence of Number Two and Number Six, Number Twelve is challenged to demonstrate that his fingerprints are Number Six's. They are. He also has his characteristic left wrist mole, which Number Six has lost. Finally, Number Twenty-four is summoned because she supposedly has a unique "mental bond" with the real Number Six, but they fail a test with the Zener cards.

Just as he appears to be "breaking", the real Number Six mentally overcomes his brainwashing when he discovers a bruise on his fingernail that he got when Number Twenty-four tried to get his picture – a bruise that, furthermore, has migrated from the base of his fingernail to midway, confirming that days or weeks have passed, not the single day shown on his calendar. He then gives himself an electric shock to reverse the therapy. He also physically overcomes the impostor, who reveals his name as Curtis. After being forced to reveal his password and remove the fake mole from his wrist, Curtis escapes and is then mistakenly killed by Rover.

Pretending to be Curtis, Number Six reports to Number Two that "Number Six is dead". Having "failed", he is to return to report failure. He is put blindfolded onto a helicopter to leave The Village. He believes himself to have duped Number Two into letting him escape, but the helicopter promptly circles back to The Village. Number Two reveals that he deduced the truth when Number Six agreed to give his regards to Number Twelve's wife, who is deceased.