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?

This is similar to my solution for Part 1.  This time, starting Farmer A walks up the right side then left across the top.  Farmer B walks the same distance left across the bottom and then up the left side.  Farmer C walks northwest to a point on the top, then walks left across the top and down the left side.

This one works out nice and evenly:

Farmer A walks 200m up and then 150m left.
Farmer B walks 200m left and then 150m up.
Farmer C walks 250m northwest, 50m left, and 50m down.

All three walk 350m which will take 175 seconds, or 2 minutes and 55 seconds.

Posted by tomarken on 2006-04-18 10:36:00