The Roxanne Problem is an episode of Peg + Cat.
The episode begins with Peg and Cat observing a pink cat admiring a pyramid-shaped pile of garbage. Cat thinks it is weird that the pink cat likes the pile of garbage so much and when Peg mentions that it is in the shape of a pyramid, Cat says, "Just because it's in a fancy shape means it's cool?" and points out how he's cool too and makes himself into different shapes. Peg thinks that Cat is acting weirdly.
After the theme song, Peg and Cat are at the beach, making a card house that they plan to make the biggest one ever, but a bouncing ball knocks it over. Cat gets angry, but Peg reminds him that the ball's owner probably didn't mean to knock over the card house. Cat agrees to return the ball but is still angry and plans to tell the ball's owner off but is surprised when he finds out that the owner is the pink cat from before. She thanks him and states that she enjoys making sulptures out of objects she finds and that it is also good for the planet because using the objects cleans up in the process. She asks Cat if he agrees and Cat, who seems to have a crush on the pink cat, nods. She puts the ball on the sculpture but it falls down and she notes that the sculpture she put the ball on always falls down if she puts more than twenty things on it. She asks Cat if he knows what would be helpful. He shakes his head no, so she explains that she wants him to count to twenty by twos every time she puts two things on the sculpture so she knows when to stop.
Cat agrees, but runs off to Peg, who's rebuilt the card house, nervously. He explains that the reason he is nervous is because he wants to help the pink cat but cannot remember how to count by twos. Peg explains that to count by twos, you count every other number. Cat counts to twenty by twos in song and wants to help the pink cat. Peg starts to continue making the card house, but Cat remembers that the last time he saw the pink cat, he got nervous and tongue-tied and is worried that it will happen again. Peg agrees to hide in the bushes and whisper a clue if Cat forgets how to count by twos and/or is too nervous to speak.
They start to sing the "Problem Solved" song, but before they can finish, Cat bumps into the pink cat, who reveals that she made the sculpture without Cat and asks what he thinks of it. He is tongue-tied again, so he nods. The pink cat says that the brick she put on top is a perfect solid shape but she has forgotten the name of the shape it's in. She asks Cat what it is and then jokingly asks if he has a voice. Cat just looks awkward so the pink cat concludes that he must have forgotten too and, while putting the brick back, tells Cat to let her know if he remembers. From behind a rock, Peg says that the brick is in the shape of a rectangular prism. The pink cat is impressed and tells Cat that he has a nice voice, is smart and knows his solid shapes. She then introduces herself as Roxanne and states that she really likes solid shapes because they have length, width and height, then suggests that she and Cat go for a walk in the woods and he can point out all the solid shapes and tell her their names.
Cat agrees but then runs back, knocking over the card house and shouting out that he has a really big problem. Peg asks Cat why he won't go for a walk with Roxanne and Cat replies that Roxanne knows so much more than him and he doesn't want her to know how ignorant he is. Peg says that Cat is so lovable that Roxanne will like him if he acts normally. Cat then sees Roxanne approaching and nervously jumps into a basket. Peg asks what to say and Cat tells her not to talk at all because Roxanne thinks Peg's voice is his voice. Roxanne asks Peg if she has seen a shy, smart, bluish-purple cat who she doesn't know the name of and Peg shakes her head. Roxanne is about to leave, when Cat says, still in the basket, "His name is Cat!". Roxanne thinks it was Peg who spoke and asks Peg if she knows him. Peg holds some cards over her mouth so Roxanne can't tell that she isn't speaking and Cat continues, speaking in third person so Roxanne will think it's Peg talking, to say that everybody knows Cat because he is famous for his vast knowledge. Roxanne says that she wishes that this smart, famous cat will go for a walk with her in the woods and asks Peg if she knows where Cat is. Peg shakes her head, so Roxanne says, "Oh well" and walks off. Cat follows. Peg asks where he is going and he says that he is going to walk with Roxanne and Peg is going to be his voice. Peg drops the cards and they run after Roxanne.
Cat carries some objects and Roxanne says that she likes painting and asks Cat if he does too. Cat opens his mouth, while Peg, who is following hidden behind the rocks and bushes, says, "Yes". Roxanne asks Cat if he likes dancing and mountain climbing. Peg says, "Yes" for him again and Roxanne is about to ask Cat about more of his likes but drops the ball from earlier that she was carrying. She identifies the ball as a sphere and walks off to retrieve it, telling Cat to wait. Peg, who is in a tree, says, "Yes" for him again, but he says that the word "Yes" is not enough for Peg to say. Peg comes down from the tree and points out that if she said anything else, Cat wouldn't know when to move his lips. Cat says that he would move his lips more, but Peg wouldn't know what to say. Peg suggests that she could sing a song and Cat could lip-synch, noting that Roxanne would like a song they know about solid shapes. Cat says that he does not know the lyrics and Peg, coming back into hiding, says that he does not need to, he just has to move his lips as she sings. When Roxanne comes back, Peg sings and Cat lip-synchs the solid shapes song and Roxanne joins in. While lip-synching, Cat dances and Peg tosses him various solid shapes.
After the song, Roxanne says that she has never met anyone who knows as much about solid shapes as Cat. Then, they bump into the pyramid sculpture from before and Roxanne says that perhaps the only person she could have met who knows more about solid shapes than she thinks Cat does is whoever made the pyramid. Pig jumps out of a nearby treasure chest wearing sunglasses and Roxanne asks if he is the artist. Pig nods and Roxanne compliments him on the pyramid and notes that it is a solid shape and that each of its sides is a flat shape. Pig sings that he loves triangles and Roxanne says that the sides of the pyramid are indeed triangles and that three triangles have joined together in a point. She then imitates Pig's triangle song and asks for permission to climb the pyramid with him. The pig just sings his triangle song again but Roxanne takes it as an affirmative and runs off to get her mountain climbing ropes. Peg pops out from her hiding spot and points out how the pig could not have made the pyramid. Ramone comes and says that he was the real pyramid-artist. Peg asks what he is doing there and Ramone says that he came to film the pig's new music video and afterwards, he made the sculpture which the pig likes because of the shapes. Pig starts to sing his triangle song again but Peg and Cat interrupt him in unison by saying that they know he loves triangles already. Ramone leaves to surf and Peg thanks him for clearing it up. Cat says that the situation is unfair because it takes him a lot more effort to make Roxanne think he's smarter than he really is than the pig. Peg says that she believes Roxanne will like Cat if he just acts like he normally does, but Cat says that he wants to "be" Peg instead. Roxanne returns and Peg hides behind the pyramid. They start to climb but become unstable because Peg is climbing on the other side. Cat shouts, "Help!" and Roxanne asks why he is speaking in the voice of "the girl [she] saw by the rock". Peg swings to the animals' side, shouting, and Roxanne asks her why she is talking in Cat's voice. They admit to their real voices and Roxanne asks why they were fooling her, speaking in third person for some reason. Cat says that it was because he wanted her to think he was smart like her. This makes her emotional, but then they start to almost fall again. Roxanne tells Pig to stop looking at his feet and Cat says that Pig cannot resist doing it because his feet are triangular. Roxanne screams and Peg "totally freaks out". Cat does his "snap out of it gesture" and Roxanne agrees with him. Peg does her backwards-counting thing and Roxanne joins in, while Cat slides down the mountain. Roxanne calls him a genius and they slide down. Peg and Roxanne start to sing the "problem solved" song but instead of singing "So everything is awesome" like he usually does, Cat sings, "Actually, the problem was that I wanted Roxanne to think I'm smart but now she won't because she really knows me, so problem not solved." Roxanne asks Cat why he repeatedly said that he was not smart. Cat replies that he says it because there are things he doesn't know. Roxanne says there are things she doesn't know as well. This surprises Cat and Roxanne agrees that they should teach each other things while dancing. Peg agrees and they sing a song about learning. Then, Roxanne says that she likes Cat, which pleases him.
In Peg's garden, Roxanne talks and Peg and Cat lip-synch a conversation, then Ramone lip-synchs and Pig sings, "You three are crazy!" which makes them laugh.
- During the theme song, Cat sinks into one of Roxanne's sculptures.
- The "problem solved" song was never sung right through properly in this episode because the first time they were interrupted and the second time Cat sang different lyrics.
- It is unknown why Roxanne spoke in third person that one time.
- Even though Cat is implied to be romantically attracted to Roxanne, it is never confirmed.