The Three Friends Problem is an episode of Peg + Cat (TV series).
The episode begins with Peg and Cat playing in the garden with Big Dog. They decide to play a game involving hopping on one leg with their tongues out and Peg charts the number of hops each one can do on a bar graph. Peg hops with her tongue out three times, Cat hops with his tongue out four times, and Big Dog impresses Peg by hopping with his tongue out four times despite it being his first go and there being mud. Cat then suggests they "crack-ulate", which is his word for making Peg laugh using his tail. He manages to make Peg laugh eight times. Then, Big Dog tries to "crack-ulate". Initially, Peg thinks his tail is too short, but then she bursts out laughing when Big Dog starts acting goofy and falling in the mud. She believes the problem of Big Dog not being able to "crack-ulate" has been solved and starts to sing the Problem Solved song. However, Cat doesn't sing along, his ears are drooping, he looks like he's crying, and when prompted, he only says a few lyrics of the song and doesn't sing it properly.
Peg thinks something must be seriously wrong with Cat and shouts that it's a big problem. The Neighbor Ladies ask Peg if she is having a problem and Peg replies that her problem is that Cat is acting weirdly unenthusiastic. They sing a song about how something is "up with Cat" and Ramone and the Pig show up, suggesting that they exercise to cheer him up. It works at first, but when Big Dog joins in and the Neighbor Ladies and Peg comment that he's good at exercising, Cat goes all gloomy again.
The Neighbor Ladies worry that Cat is getting sick, so Peg puts him to bed and starts to read him Puss in Boots, with Big Dog acting the part of Puss in Boots. Cat doesn't want to hear the story, so Peg freaks out because that's very out of character for Cat. Big Dog holds his paws up as if to say, "snap out of it" and Cat then states that it's his job to stop Peg from freaking out. Peg asks Big Dog to leave so she can talk to Cat, then asks Cat if he thinks she likes Big Dog more than him. Cat says yes, and draws a graph stating that she used to love him up to infinity but now she loves him only a little bit and she loves Big Dog up to infinity. Peg tells him that she doesn't love him any less and they sing a song, along with Ramone and the Neighbor Ladies, about how friendship/love can't be measured and they're all good friends.