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The Order of Lines

Arrange N points evenly around a circle. Label them A,B,C... clockwise.
Starting at point A, draw
a continuous path of lines, visiting each point once and finishing at
point A. For N=3, there is only one figure which can be drawn (a triangle),
regardless of the order the points are visited. For N=4, there are two
different figures: a square (ABCDA), and a cross with two sides (ABDCA).
[Although a rotated version of the second figure can be drawn (ACBDA),
we consider them identical.]
Disregarding rotations and reflections, how many different figures can
be made for

- N=5?
- N=6?
- N=7?

Source: Based on a problem from
The Little Giant Encyclopedia of Puzzles.

Solution

Mail to Ken