I hope this is the right plcae to post it as I'm not sure if the solution is mathematical. I saw this riddle on a board at the university and it seems that there's something I'm missing. It goes as follows:
As cat and a mouse are running on $10m$ circle at speed of $1\frac{m}{s}$. They can each change their direction in notime. Will the cat catch the mouse?
I can't see why the mouse can't change its direction everytime it goes near the cat, but I guess this is not the answer.