Spiked Math: MFT - Lake Escape

Greg Bernhardt

** Sorry about the music, I don't know how to stop it and still show the game on this page -- hit the mute button in the bottom right of the game to shut it up! **

Math Fact Tuesday! More of a puzzle, but if I give you the answer it'll become a fact, right??

This puzzle (credited to Martin Gardner) can be stated as follows (text source):

We are in a rowboat in the center of a circular lake. On the edge of the lake is a mean goblin who wants to eat us; and if he catches us, he will do so!! The goblin can't swim and won't go into the lake (and doesn't have a boat), but he can run K times as fast as we can row.

We, however, can run significantly faster than the goblin can, so if we are able to reach a point at the edge of the lake without the goblin being there, then we will be able to escape.

Question 1a: For K = 1, is there a strategy we can use to escape?

Question 1b: What about K = 3? or K = pi? or K = 4? or K = 5?

Question 2: What is the best possible value of T so that:

if K>T then the goblin has a strategy to catch you (and eat you),
if K

Jonathan Scott

The above has been truncated at a point where the original contained "<=", so I guess something odd has happened at the HTML or XML level.