Hi joet, wileysw,I heard the problem from a friend who came with it after he visited Cambridge University, so the rumor might be true. I personally didn't try to solve it in half an hour, I put it on the back of my mind, but I gave my friend the solution the next day. He said the solution is wrong. I thought about it some more, and I came with a different answer. We both agreed that the second answer is the "correct" one. However, it turns out you can ask the problem in two ways: either you can form a tight knot in the rope, or you can't. If it's a lasso where the knot can glide, then the problem is slightly more amusing; that's the reason I proposed that there is no friction. So to summarize, here are the 2 problems: 1. what's the critical angle assuming you can make a tight knot2. what's the critical angle assuming the knot glides without frictionFor the first problem, Joet's plan of attack is perfect, but, as wilesyw mentioned you don't need to do any calculations since the surface can be flattened. For some reason I am not getting 30 degrees for either problem, but I'm hesitant to say that wileysw is wrong. I'll get back and think about the problem some more myself. Best,V.