2 [Arithmetic. Mental calculation, etc.]

"Turns right - starts a song, turns left - tells a tale". To tell a tale, the Scholar Cat needs 5 minutes, and to sing a song - 4 minutes. At 10 a.m., the Cat started telling a tale. Which way will the Cat be going at noon?
To tell a fairy tale and sing a song to the Scholar Cat, it takes $4+5=9$ minutes. From 10 AM to noon -120 minutes. $120=9 \cdot 13+3$. This means that during this time, the Cat will manage to sing 13 songs, tell 13 fairy tales, and have 3 minutes left to start (but not finish) telling a fairy tale. And this means that at noon, the Cat will be turning left.