In flashback sequences to the last episode, Gideon address a class at the FBI Academy discussing the "Footpath Killer" who leaves Polaroids of his victims at his crime scenes in Virginia. Gideon's profile describes the unsub as a white male in his twenties who owns an American-made truck and works at a menial job. "When you find him, don't be surprised to hear him speak with a severe stutter." Gideon himself is pulling into an old-fashioned gas station in Dumfries, Virginia, and is confronted with the very profile he has just given – and as the young man gives Gideon his change, he stutters, "Have a nice day." Gideon hesitates, staring at the young man and a wall of Polaroid pictures behind him before walking out of the gas station. The man has noticed Gideon's gun and threatens him with a shotgun, insisting Gideon tell him who he is. When Gideon reveals he is with the FBI, the gunman gets even more agitated, demanding to know what Gideon knows. "I know how you do it, I know you can't stop and I know something that no one's ever been able to tell you. I know why you stutter."
Gideon is relating this story to a small group of cadets in his office, and admits to being very scared at the time. He mentions James Reese who once said, "There are clues at a crime scene which, by their very nature, do not lend themselves to being collected or examined." Elle leans into the office to hear Gideon tell the group that some killers are still caught by dumb luck. As the cadets leave, Elle asks Gideon why the Footpath Killer stuttered. Gideon challenges her to figure it out herself.
Walking through the BAU bullpen, Gideon approaches Reid's desk and makes a move on his chessboard. "Check. Checkmate in three moves." Reid is startled, and Morgan advises that Reid will beat Gideon when he starts learning to think outside the box. Elle brings the question about stuttering to Morgan and Reid, who also don't know the answer. JJ enters and introduces herself to Elle. Hotchner asks the team to meet him in the conference room.
At the round table, the team discusses a video they have just received from a student at Bradshaw College in Tempe, AZ, where they have had 6 fires in 7 months. The video shows a fire in a building across from the students' dorm. The camera pans to the dorm room door, where the boy's roommate, Matthew Rowland, sees a fluid coming in under the door. He stands in the puddle, and sees the doorknob turn before the fluid catches fire and engulfs the boy.
On the BAU plane, the team discusses serial arsonists who are typically white males between 17 and 27, and are set off by loss of job or loss of love. The fires at the college are becoming more frequent, and the arsonist has killed for the first time. Arriving at the college, Gideon advises the team to be casual – "Try not to look official." The Dean and the Fire Inspector tell the team several bottles of flammable material are missing from the science lab. They may have to evacuate the college.
Reid and Hotchner examine the dorm room where Matthew Rowland died. It doesn't make sense that the arsonist couldn't see the fire inside the room as he needs to experience the fire. The other fires had been set with simple devices, but the last fire was set manually. The team discusses motives for fire: vandalism, crime concealment, political statement, profit and revenge. None of these seem to fit the last fire.
Morgan goes to the dormitory to role-play the best way to set a fire. Setting the fire on the third floor doesn't make sense if the unsub's target was the building. Elle and Reid discuss whether the unsub is a chemistry student or a chemistry professor – Elle bets on a student – he would be less confident and arsonists are socially incompetent. Gideon and the Dean walk through the college, discussing the tip line Gideon has set up hoping the arsonist will call. Gideon notices that the sprinkler system in the building doesn't seem to be working and the water fountain nearby is broken. Meanwhile, a professor entering his office notices a fuel smell. Gideon pulls the fire alarm to evacuate the building and runs inside. The professor turns on the light and a light bulb blows up in his face. Gideon tries frantically to put the fire out with a fire extinguisher nearby as Morgan races into the building and physically wrestles a resisting Gideon outside and down the steps. He couldn't have saved the professor.
Hotchner advises Elle to take pictures of the crowd surrounding the burning building, assuming that the arsonist will be there admiring his work.
As the team meets to discuss the situation, a chemistry student, Jeremy, tells the Dean he and some other students know how the unsub set the last fire. The team has been discussing the case all night and they have nothing. The pictures of the students at the fire reveal only horror and fright. Elle mentions the "homicidal triad," the three behaviors in childhood that often point to disassociative criminal behavior in adults – fire starting, bed-wetting and cruelty to animals. The standard profile of a serial arsonist is not helping them.
Gideon goes outside and is confronted by a student patrol on a bicycle. The student mentions his skepticism of profiling, but becomes a believer when Gideon tells him his girlfriend is afraid he is about to break up with her.
At the chemistry lab, Hotchner and Reid are talking to the chem lab assistants. Reid is uncomfortably going on and on about the BAU when Hotchner interrupts and asks the students what they know. Jeremy describes an easy incendiary made with light bulbs and gasoline. Another student, Clara, tells the team the three simple ingredients useful in making a Molotov cocktail. Jeremy leaves with Reid and Hotchner, explaining that they need an elevator key to use it after hours, and discusses his project on the Three Body Problem.
Back at Quantico, JJ and Garcia are listening to a recording on the tip line. The team listens to it again and again, but the garbled voice is no clearer. It sounds something like "I do this for Karon." Garcia will put the recording through more filters and try to get the sound clearer as Elle and Morgan begin interviewing all the Karens on campus. Out on the quad, Gideon encourages Reid to think outside the box - the box, in this case, being the standard profile of a serial arsonist. Sometimes they have to get creative and think of unlikely things – like a stutter.
Gideon finds himself in the science building looking at posters concerning the Three Body Problem, one of the great mathematical mysteries. The same student patrol enters and tells Gideon he broke up with his girlfriend to date someone new. "Brian." His girlfriend took it well except for telling him "Homosexuality is a sin and I'm going to incur the wrath of God." This leads Gideon to think a different way about their case.
Garcia can now tell the caller isn't saying Karen, the word may be a Hebrew word for God's burning anger. God is fire in many religions; the unsub may be punishing the students for their sins, or performing baptisms by fire. Gideon cautions the team not to jump to conclusions. Reid mumbles, "Compulsion," and heads off to examine the original video in detail, watching it again and again. He is consumed with thinking "outside the box," and Gideon encourages him to try to look "three moves ahead," like in chess. Slowly, Reid puts the pieces together.
The unsub suffers from an Obsessive Compulsive Disorder called "scrupulosity", and is obsessed with the number three. The doorknob turned against the lock three times, three fires were set at once, the first fires, the single fires, were in a trinity of threes – one at 3pm on March 3rd. The convergence of threes leads to anxiety and the OCD sets fires to ease that anxiety. The professor killed was in office #3. His met on Tuesdays, the third day of the week, and Matthew Rowland had that at 3:00 pm. Hotchner remembers Clara Hayes from the chemistry lab, who repeated the same word three times, and kept turning her ring around in intervals of three. She was one of the students working on the Three Body Problem.
Elle and Hotchner go to Clara's apartment and find it filled with religious ramblings and quotes, candles and photos of fire. They find multiple containers of flammable liquids and evacuate the building. Hotchner finds an article about Clara's childhood. Her house (number 333) had burned down and only Clara survived. Her mother said "My child was tested by God, He tested my child and she came through blessed."
The campus is being searched for Clara – for any convergence of threes where she would feel she would need to start a fire. Security teams turn on the fire alarms in every building. The three chemistry lab assistants are taking the elevator in the science building when the power goes out. Clara has stopped the elevator on the 3rd floor. Pushing the elevator doors open, the three are at first relieved that Clara is there, but her strange behavior scares them. Clara sprays the three students with fuel, telling them God has chosen them to be tried by fire.
Reid and Hotchner warn Gideon not to try to reason with Clara, she isn't setting these fires because she wants to, but because she has to. They know it is in his nature to try to get Clara to stop instead of using force to stop her.
The team is running out of places to search when Reid tells Gideon the third floor of the science building is under construction and he and Hotchner head there. When Hotchner arrives he finds Clara holding a lit flare, and getting ready to throw it on the three students. He tells Clara to resist her compulsions, and that she wants to stop, but she can't so he shoots her in the leg. Gideon says, "I thought you said not to reason with her?"
Back on the BAU jet, Elle tells Gideon she realizes he had no idea why the Footpath Killer stuttered, no one could know. He was just trying to stall him as Hotchner was trying to stall Clara. Gideon tells her the rest of the story: he was trying to provoke a stutter.
The Footpath Killer forced Gideon down a hall into a small room. In the room were pictures of his many victims – more than law enforcement had found. Gideon intentionally demeans and insults the killer, getting him more and more agitated and making his stutter worse. Making fun of his stutter angers the killer and he takes his eyes off Gideon just long enough for Gideon to grab the gun and get control.
On the plane, Reid and Gideon are playing chess. Reid confidently asserts, "Check in three." Gideon tells him that's not bad, but he can see four moves ahead, and still beats him.