You are in a boat in the exact center of a perfectly circular lake. There is a goblin on the shore of the lake. The goblin wants to do bad things to you. The goblin can't swim and doesn't have a boat. Provided you can make it to the shore — and the goblin isn't there, waiting to grab you— you can always outrun him on land and get away.
The problem is this: The goblin can run four times as fast as the maximum speed of your boat. He has perfect eyesight, never sleeps, and is extremely logical. He will do everything in his power to catch you. How would you escape the goblin?
Follow up: What is the minimum speed of the goblin (relative to your boat) such that escape becomes impossible?
Answer: First of all, row out to a radius R/4 (where the lake has radius R) keeping you, the centre of the lake and the goblin in a straight line - with you on the far side to the goblin . This is always possible; radius R/4 is the first point where the angular speed you can achieve just matches that of the goblin as he runs round to get you.
You are now a distance 3R/4 away from the shore, directly opposite the goblin so he needs to run a distance πRπR to get you. You will take time 3R/4V at speed V if you now row directly towards the nearest shore, and he will take πR/4V, which is fractionally greater.
For the followup: If instead of 4×, the goblin runs N× your speed... then you row out to radius R/N, you then take time (N−1)R/NV to reach shore and he takes πR/NV to reach the same point. You escape provided that N<π+1≈4.1459
Source: stackexchange
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