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Problem of the Week 933

Ultra Zigzag

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Consider polygons with 10 sides in which we allow sides to intersect. Each intersection point can be an intersection point of two edges only, not three or more.

Find such a polygon with the largest number of intersections.

Consider the same question for a polygon with n sides.

  1. Is there a formula for the maximal number of attainable crossings when n is odd?
  2. Is there a known formula when n is even?
Source: Sigbjorn Vik, Macalester Student

© Copyright 2001 Stan Wagon. Reproduced with permission.

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30 Mar 2001