The Mountain says they think it was an infiltrator from the Brotherhood without Banners, whoever they are. Tywin is vexed, and wants them all dead. The Mountain says it will be hard to find them. Tywin says to just burn all the villages and farms in the area. See, that seems like an easier plan than all this person-by-person interrogation. Arya lays out some mutton and appears to consider stealing a knife. Tywin says he doesn't like mutton, but has her leave it. He tells her to eat, and she wants to eat in the kitchen later. He tells her, "It's bad manners to refuse a lord's offer. Sit. Eat." She does. He tells her she's small for her age, but she assures him she eats a lot. Now he's in a contemplative mood and turns toward the window. He says this will be his last war, win or lose. And of course, he's never lost. He says it's already being called the War of Five Kings (Joffrey, Robb, Renly, Stannis, and... Balon? I guess he's known publicly now that Theon has Winterfell), and his legacy will be determined in the coming months. Arya considers stabbing him in the back.
Tywin defines "legacy" as "It's what remains of you when you're gone." Then he tells her about Harrenhal, which had the tallest towers and strongest walls. Now it's a blasted ruin. What happened? "Dragons happened." The problem was that Harrenhal was built to withstand an attack from the land. Tywin says, "A million men could have marched on these walls and a million men would have been repelled." Instead, Aegon Targaryen changed the rules (attacked with dragons), so everyone knows his name 300 years later. Arya points out that Argon's sisters Rhaenys and Visenya were also riding dragons. I like that she's more interested in the women. She provides biographical information: Rhaenys rode Meraxes. Visenya rode Vhagar. Tywin: "I'm sure I knew that when I was a boy." I also like that she can't remember noble houses and sigils, but she's good at who rode what dragon. Arya talks about how great Visenya was. Tywin asks if girls aren't supposed to be interested in pretty maidens from songs. Arya utters what might as well be her motto: "Most girls are idiots." He asks where she learned about Visenya and her Valyrian steel sword. She again claims it was her father. Tywin observes that he's never met a literate stonemason. She shoots back, "Have you met many stonemasons, my lord?" He glares at her and says, "I enjoy you, but be careful." He has her take the food back to the kitchen and eat it there. And he tells her that lowborn girls say "M'Lord," not "My lord." Arya claims that her mother served Lady Dustin for many years. And as a result: "She taught me how to speak proper -- properly." Tywin tells her she's too smart for her own good. She admits that she's been told that before.