This was passed to me haphazardly, so I apologize in advance for any mistakes.
You are on a circular lake in a boat. There is a monster at the edge of the lake, waiting to eat you, who can't go in the water. You must reach shore before he reaches you there; then you are safe, regardless of how close he is to you. You can row at speed x, but he can run at speed 4x. What do you do?
NB: assume the monster pursues its optimal strategy, which is to move always to the point on shore to which you are closest.
EDIT: https://puzzling.stackexchange.com/questions/2155/the-lake-monster
Negotiate effectively with the monster. Focus on interests not positions.
The monster's position is: I will eat you if you reach the shore and I am there when you get there.
Find out what the monster's underlying interest is. Is it hungry? Is it interested in real power, or only in appearing powerful because it has to maintain its monster image and fears ridicule? Maybe the monster simply craves variety and is sick of fish. Does it speak your language? Maybe it's lonely.
Get as close to shore as you can but still stay out of reach. Let the monster know that you would like to begin a negotiation and try to uncover the monster's interests.