Number Six is having coffee at a café when he sees a helicopter arrive at the Village. He also notices a man covertly watching him. A loudspeaker announcement says that "the General" wants all students participating in the three-part history course to go home to watch a lecture on television presented by the Professor. Every person in the vicinity leaves except for Number Six and the man watching him. The waiter closes down the café and tells Number Six that it is time for "Speedlearn." The watcher, Number Twelve, approaches and discusses the fact that the course is designed to give a university-level three-year degree in three months. Number Six is skeptical but doesn't discount it. Number Twelve suggests that he might enroll in the program. They're interrupted when they see an elderly man running away from the helicopter with a mob in pursuit. Number Twelve identifies the man as the Professor and leaves. Number Six goes to the beach and finds a tape recorder that the Professor drops. He plays it and hears the Professor beginning an urgent warning. Before he can listen further, Village Guardians arrive and Number Six hides the tape player. They offer him a ride back to his flat to listen to the lecture. As they go, the mob catches up to the Professor and drags him back.
At his flat, Number Six tunes into the lecture and the Professor's wife appears to apologize for her husband for running late. She starts to talk about Speedlearn but the Professor arrives and boasts of how successful Speedlearn is and how it will revolutionize education. He talks about how he was skeptical of the workability of Speedlearn but then he met the General who made it all possible. The announcer tells the audience to simply watch and relax and an image of the Professor appears on-screen. Number Six blanks out for fifteen seconds and wakes up, startled.
Number Two arrives with an assistant who scans the flat for the tape recorder. Number Two says they're looking for the Professor's lecture notes but Number Six denies having seen the tape player. Number Two offers Number Six his freedom in return for the tape player's return but Number Two pleads ignorance. Number Two then asks Number Six several questions on European history, the subject of the lecture. Number Six rattles off facts and figures and Number Two recites along with him, and then departs. Number Six calls the operator, who can recite the exact same information. He then goes to the beach to get the tape player only to discover it's gone. He finds Number Twelve watching him and demands to know what's going on. Number Twelve shows him the tape player and notes that Number Six could have used it to buy his freedom. He goes but as he departs he asks Number Six a conceptual question about European History, and Number Six discovers he can't answer it. He then plays the tape: the Professor warns that people are being enslaved by Speedlearn and they must destroy the General.
The next day, Number Six discovers that everyone in town can recite the information implanted in his brain. Number Two is busy assuring his superiors that the Speedlearn test project is going well and that the Professor will be all right after several days of rest. Number Twelve, his underling, arrives and suggests that the Professor is a troublemaker. Number Two warns him to keep his opinions to himself. He then warns the doctors not to distract the Professor from writing his next lecture. As the doctors take the Professor away for therapy, one of them feeds his lecture into a scanner and converts it into a computer strip.
Number Six attends an art seminar held by the Professor's Wife. He tires to steer the conversation toward the General but she refuses to respond. Once she leaves, Number Six slips into her and her husband's private house and finds a room filled with busts. She comes in and demands to know who he is and he wonders how she and her husband have earned their special privileges. Number Two comes in and the Professor's Wife denies any connection with Number Six. The doctors bring the unconscious Professor in and put him to bed, but Number Six uses a walking stick to smash in his head: the "Professor" is a dummy. He then tosses the tape player to Number Two and leaves. The head doctor is worried and Number Two tells him to mind his own business.
As the Villagers celebrate the success of Speedlearn, Number Six walks through the streets and notices Number Twelve. Number Six returns to his flat but the lights short-circuit. A repairman calls and tells him to wait for someone to arrive. When the repairman does arrive, he determines that someone sabotaged the lights. Number Twelve visits and tells the repairman to go get batteries, then has a secret conversation while the surveillance devices are shorted out. He gives Number Six a pen with a microstrip inside as well as two electro passes. He tells Number Six to get the Professor's true message on the strip out tomorrow at the next demonstration. When the lights come back up, he warns Number Six against sabotage and departs.
The next day, board members are arriving at the Administration Building where the demonstration is to be held. Number Twelve, in charge of administration is there, and Number Two examines the microstrip with the Professor's next programmed lecture and declares it satisfactory. Among the board members is a disguised Number Six.
Number Two takes the microstrip to the projection room and orders it made ready for transmission. Number Six uses an electro-pass to enter with the other board members and then slips away. Number Two then addresses the board, having Number Twelve explain Speedlearn. Number Six knocks out the guards at the projection room, then slips inside and takes out the projectionist. However, during the struggle Number Six is stabbed in the arm. He places the real microstrip in the project device while in the boardroom, Number Twelve explains that Speedlearn lets them place anything they want in the human brain. Number Two scans the facility for a final check and spots Number Six due to his bleeding arm. With seconds to spare, a guard knocks out Number Six and makes sure the intended transmission goes out.
Playing along to maintain his cover, Number Twelve demands answers from Number Six. Number Two warns that Number Six is tougher than that. The Professor's Wife calls to ask if she can see her husband and Number Two uses the Professor as a lure to keep her obedient. He concedes that he needs the Professor and his wife to maintain each other's loyalty to the project. Number Two then prepares to visit the General and ask him who Number Six's co-conspirators are. They go to a study where the Professor is working on another lecture. He converts it to microstrip and enters a large chamber that contains... a computer. Number Two explains that the computer is the General and they can use it to calculate any problem, and implant any thoughts they want via Speedlearn. He has the Professor prepare a microstrip with a new problem: who is the traitor who gave Number Six the electro-passes?
As the Professor prepares to enter the microstrip, Number Six says that he can stump the General. Number Two challenges him to do so and Number Six types out a single four-character message on a piece of paper. He then converts it to microstrip and has the Professor feed it in. The computer starts to smoke and overheat. The Professor tries to shut it down and is paralyzed by an electrical current. Number Six takes on the guards while Number Twelve tries to pull the Professor free, only for both of them to be electrocuted.
The General explodes and Number Two surveys the destruction, then turns to Number Six and asked him what the question was. Number Six says that he gave it the one insoluble question, to man or machine: "Why?"
Later, Number Six visits the Professor's Wife and gives her the news about her husband.