A Puzzle

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The star puzzle

How many hexagons can you find in this figure?

A hexagon is any polygon whose boundary can be traced by moving along the line segments shown; the boundary must form exactly six proper angles to be a hexagon.   (A "proper" angle is one that is not a multiple of 180 degrees.)  Furthermore, the removal of any finite number of points must not disconnect the hexagon.  (This rules out solutions involving  two triangles touching at a single point, for example.)

To get you started, here are a few of them (shown in dark cyan):

For some hints, see the "Ask Dr. Math" forum.  Our final hint: there are far more than 19.

Solutions

Link here for the answer.
Link here for a display of all polygons in the figure (372 Kb--about two minutes to download).
Link here for an explanation of how we used GIS software to develop these solutions.

Check out science-->earth science-->GIS at
  

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Last modified: Thursday October 05, 2000.