The right brain to Peg's left brain, Cat approaches problems the exact opposite of the way Peg does. When trouble rears its head he yawns. Lies on his back. Has a snack. Wrestles with a twig. Makes up a silly song. Or curls up on the nearest ball and takes a nap!
Though Peg leads the problem-solving most of the way, at some points in each show she reaches a dead end. That's when Cat does some apparently trivial thing – nibbles on pie, sings a ditty, or curls up into a shape that reminds her of something from earlier in the show – and this little thing he happens to do triggers a connection in Peg's mind that shows her the way to a solution!
In their lopsided, quirky way, this team of two totally works. Peg without Cat could never quite get there. But Peg + Cat = Total Triumph Every Time!