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On the 100th episode, Barney must choose if he should give up wearing suits in order to land a hot bartender, but his conflicted feelings result in an amazingly awesome musical number. Meanwhile, Ted gets closer to meeting the future mother of his kids.
Ted: (Describing an awesome girl he just met) She's a PHD-candidate, she reads philosophy for fun, she does the Sunday crossword every week - and finishes it!
Barney: Wow, Ted, I am so happy for you! Sorry, not for you, happy I'm not you.
Lily: Baby, you don't have to pretent other women aren't attractive just for my sake.
Marshall: I know. And if that women were anywhere near as hot as the woman I'm married to, I'd admit it, but she's not.
Lily: Baby, you're so sweet, but compared to that woman, I am a big bag of three day old garbage.
Marshall: Well, I call 'em like I see 'em, and I just think you're the most beautiful woman in the world.
Lily: See, that's just annoying!
Cindy: I thought you were a complete idiot. But a cute idiot.
Ted: So, do you ever date cute idiots?
Cindy: Almost exclusively.
In Barney's apartment, the bartender's hair is curly, but when she leaves at the beginning of the musical number, her hair is straight.
Ted works for Columbia University. Cindy tells him that University policy prevents them from dating. According to Columbia University: "Consensual, romantic relationships between faculty and other employees and students and between individuals who work together are generally not considered sexual harassment and are not prohibited by University policy."
Cindy says she was in the class when Ted started teaching the wrong class on his first day as a professor. This happened in episode 5x01 "Definitions".
Future-Ted: ...and your mother got her yellow umbrella back.
Ted gets this umbrella after "the mother" (who he has yet to meet) left it behind at a bar in episode 3x12 "No Tomorrow".
Robin laughs when she says that she doesn't think she is the hottest girl in the bar. We learned in episode 3x14 "The Bracket" that Robin tends to laugh to cover up a lie.