Hosted by The Math Forum

Problem of the Week 933

Ultra Zigzag

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.

30 Mar 2001