Tuesday, October 19, 2010

The Circular Lake Monster Problem

Problem:

For #1, how about row in a circle a bit smaller 1/4r in size. Since he won't be able to keep up with you, when he is on the opposite shore you can make a brake for it. You have r*3/4 to travel, but 4*3/4 is less then pi, so he won't be able to catch you in time

Solution:

Assume x is the monster's speed. Then to get the circle trick to work, you row a circle a little less than 1/x of the radius, leaving you 1 - 1/x to row when he is opposite of you. If the monster can travel pi times the radius faster than you can travel the radius, you're hosed. In the time you travel 1 - 1/x, he'll travel x times that. Set that equal to pi, and you x * (1 - 1/x) = pi, which solves to x = pi + 1.

pi + 1 would be my guess for the speed that impossible to escape from, but I could be making an easy mistake.

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