Three neighbours buy a piece of land that they want to cultivate as a garden. The land has the shape of a square. To avoid that their petunias and pumpkins get in the way of each other, they decide to split the garden into three cells of equal area. To keep things simple, the border between two adjacent cells should be a straight line. Under these constraints, can you help them to divide their garden such that the total length of the fence is minimized? How would you divide the garden for five, six, seven or eight neighbours?
If Charlie's method was adapted for all numbers of neighbors, then the fences should be placed as to cut the perimeter in equal pieces, which is established in "Let them eat cake", pid=5138. (Note that this is not equal to dividing it into equal-degree areas) The problem now is to figure out where to start one fence.
Posted by Gamer
on 2006-12-28 12:45:43