Three Cottages Problem
|Three Cottage Problem|
Three Cottage Problem
- The three cottage problem is a problem in graph theory.
We have three cottages, represented as rectangles, and three wells, represented as circles. Each cottage requires an individual road to every well, but bad blood between the cottage owners requires that no two roads intersect.
The problem is simple; can the roads be drawn in such a way to meet these conditions?
Keep in mind that the cottages are a completely 2 dimensional plane; clever use of bridges or tunnels are not allowed. Likewise, a road cannot be built through a well or a house.
It is highly recommended that you attempt to work out this problem yourself before seeing the solution.
Interactive Flash App
Draw lines from the houses to the wells and see for yourself how this problem works:
The problem can be solved if it takes place on a torus. While technically the problem is still on a two dimensional surface, the two dimensional surface exists in a three dimensional space.
Ideas for the Future
Better pictures in general.
A interactive animation of the torus solution. The user should be able to rotate the torus to see how the lines are drawn.
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