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?

(In reply to idea by Charlie)

I assumed that one of the fences would be along the center up to a point and then fork to opposite sides. If piece of land is a unit square we can minimize the internal fence to 1.635 units by choosing a point 0.602 units which gives an angle of 104.5 degrees.

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Edited on December 27, 2006, 4:22 pm

Posted by Eric on 2006-12-27 16:18:16