Pentalpha

Pentalpha is a puzzle where the goal is to place nine stones on the ten intersections of a pentagram. The puzzle is used as a confidence trick in Mexico, where it is known as estrella mágica. The following rules need to be obeyed when placing the stones:
 * 1) The stone has to visit two other points before reaching its final point.
 * 2) These three points have to be next to each other.
 * 3) The points have to be in a straight line.
 * 4) Although the second (middle) point is allowed to be occupied by a stone, the first (starting) and third (ending) points must be clear before a stone is placed at the third (ending) point.

Solution
The solution to Pentalpha can be found for any starting point using the following algorithm:
 * 1) Choose a node X.
 * 2) Travel two nodes in a straight line to node Y.
 * 3) From node Y, place a stone at node X.
 * 4) Let node Y be the new node X.
 * 5) Repeat step 2-4 until the puzzle is solved.