- Harold reluctantly agrees to help John protect a young woman who is participating in a dangerous game, meanwhile Shaw continues her extra curricular activities.
- Reese is getting buried under the paperwork in his undercover identity as Fusco's partner, and Shaw is adjusting to her new undercover identity as a street level criminal. As such, Reese foists off dealing with the latest number to Finch, who still is hesitant to continue such work. Finch decides at least to start the process if only because the number is akin to someone like him. She is college sophomore Claire Mahoney, a seemingly brilliant young woman with an analytical mind. However, her life seems to have fallen off the rails in the past year, ditching her college studies and having recently purchased a firearm. As Finch tails her, he believes that she is involved in some deadly code breaking game/puzzle, the puzzle which always involves the figure of a nautilus. In addition to tailing her, Finch also tries to figure out who set up the puzzle and what its purpose is. Eventually Reese, Shaw, Root, Fusco and Bear get involved in helping Finch to varying degrees. What they collectively discover is that what happens to Claire has an indirect bearing on their own survival.—Huggo
- After the bust of the Brotherhood's drugs, Reese is promoted and transferred to the Homicide Department and becomes Fusco's partner. Reese receives the number of college student Claire Mahoney, and the reluctant Finch helps him. He says that she was a brilliant student, capable to play chess with and win simultaneously three A.I. until the last year when her life turned upside-down, and she bought a gun. Soon Finch learns that she is playing a dangerous game made by the Samaritan, and she has hacked its competitor, Silverpool, and stolen important files. Silverpool's operatives are hunting her down and Reese and Shaw are protecting her. But life is made of choices and Finch learns it from Claire.—Claudio Carvalho, Rio de Janeiro, Brazil
- We open with Finch working in the underground area he's just found. He gets a message to meet Reese at a diner, but it turns out he just wanted to connect Finch with the newest number, Claire Mahoney. Claire is a brilliant mathematics major who excels in chess and with computers. Suddenly in the last two days she's been caught trespassing and breaking into cars, and has purchased a handgun.
We see Shaw at the scene of her first heist with the gang of jewelry thieves she's decided to join as her cover. Root swings by and reminds her she'll be safe so long as doesn't get caught and doesn't stand out.
Finch follows Claire as she pull a "Lost Dog" number off a telephone poll. There is a nautilus shell on the paper. Finch eventually figures out the numbers are part of a math equation that forms GPS coordinates in New York. Finch finds Claire staring at a large piece of street arts which also features shells. Claire sneaks up on Finch and pulls a gun on him. She asks him "Are you playing too?" She shoots a passing car, blames it on Finch and takes off. Reese shows up to bail Finch out of trouble. He tells Reese he thinks she's playing some kind of game and is a danger to herself.
Reese goes to Claire's apartment and finds an extra hard drive hiding in a book. While he's there, Claire's father Doug shows up looking for his daughter. Reese tells Doug his daughter's fine.
Finch shows Reese a picture of Claire with the graffiti. It's also a puzzle. The men figure out it points to another location.
While Reese waits at the next stop in the puzzle Finch looks through Claire's hard drive. Claire arrives and is standing in the middle of traffic. Reese knocks her out of harm's way, just as Doug arrives. At this point Finch tells Reese that Claire's parents are both dead. The man claiming to be her father Doug is some type of operative for a military contractor. Reese fights him and a partner off as Claire gets away.
Finch figures out there have been two previous "games," each one approximately a month apart. He has no idea who is behind the game, but it is somebody powerful. Finch deciphers the clue Claire was checking out in the street.
Claire confronts Finch in the street at her next stop. She knows he has her hard drive. Finch references the eulogy she wrote for her parents and says he's there to help her. It doesn't work.
Finch asks Shaw for help with Claire. Using security camera footage he traces the original "Lost Dog" sign to a nearby barista. Shaw roughs the guy up, but all he tells them is an anonymous email told him to do it in exchange for money.
Reese follows Claire into the latest game locale, a biker bar. She's looking at several patches on the wall. Reese sends the picture to Finch. At this moment Finch's laptop is "hacked back" and he's forced to throw the computer out the window and tell Shaw to take off. Finch is convinced this means Samaritan is the creator of the game. Against Finch's advice Reese follows Claire and saves her from several more operatives of the contractor. He is able to subdue all of the man and save her.
Root tells Finch she thinks Samaritan is using the game to recruit human assistance. She thinks the computer wants Claire because she'll help without asking questions. She says that at some point people need to choose for themselves.
Reese is able to get the men to tell them they work for a contractor called Silver Pool. Claire was able to hack their network and take sensitive information, likely enough to get the operation shut down.
Fusco helps Reese figure out the biker patch. It turns out to be a song indicating the next stop is the observation tower at Rockefeller Center.
At the next game location Reese takes out a sniper who had Claire in his sights. Shaw joins up and they take out two more Silver Pool operatives. On the roof Finch has a long conversation with Claire. He want her to quit the game, explaining it's on behalf of a "dangerous force." She references the death of her parents and say she's looking for meaning in life. Finch pleads with her, saying this isn't the meaning she needs. Eventually Claire disappears. Reese and Shaw arrive. Finch says "Claire will figure it out for herself."
Claire goes to the final locations of the game. She is surrounded by Silver Pool operatives who ask her to turn over the stolen files. She is ready to give up when unseen snipers take the men out. She hears a noise and spots a Smart Phone-type device, just like the one Greer uses. It tells her "I will help you now."
We find out that Silver Pool had been developing a program that would have been a competitor to Samaritan. The game was serving a purpose. Reese tells Finch that Claire hasn't arrived back at her college.
Finch brings him to the underground area he's discovered. It's an old subway repair line, built in the 1930s and now abandoned for decades. Finch will be able to use underground fibers to avoid Samaritan and resume operations with the numbers. The team is back.
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