Long ago, I stumbled across the following problem: Assume we have a square with length of the of 1 located in the origin of the coordinate system. Let's have a mouse in the origin (0, 0), too. Let's have a cat in the neighbor corner (1, 0). This is at the time t = 0-. At t=0+, both cat and mouse start moving. Mouse always moves along y-axis with constant veocity v << 1. Thus, after some finite time tm = 1 / v it will finish its journey in (0, 1). The mouse "wins" if it comes there before Cat, however, wants to stop it in achieving this. It is moving twice as fast (2 * v) and is always moving towards the mouse. That is, vector vc of the cat's speed is always directed to the (0, ym), where ym is the current position of the mouse. If the cat catches a mouse, it, of course, "wins" the game. Who will win? It's not a life matter, but I would really like to find the solution to this. I tried some computer simulation and got some results, but I need some kind of mathematical-only proof. Thanks for any replies!