Four farm-hands need to walk the entire perimeter of a very large square field to check the fence posts. They can each walk separately but every section of edge needs to be walked by at least one person. The field is 200m on an edge and they all start at the same corner and can walk at 2m/sec. They do not need to finish at the same place and they may cut through part of the field if necessary (and they walk at the same pace if they do).

What is the shortest time in which they can check the entire edge?

How long would it take if there were only 3 farm-hands?

Consider the same problem with a circular field of radius 100m.
How long would it take to check the entire perimeter with 4 farm-hands?
With only 3?

(In reply to solution by Charlie)

Good job Charlie!  Once I saw that you had beaten me to the punch on the circular field, I gave up on that part.  I'm just relieved to see that my solutions for the first two parts matched yours! :)

Posted by tomarken on 2006-04-18 13:22:45