A pentacle consists of 5 straight lines as shown above. A node is where any two of these lines intersect or meet. Therefore, a pentacle has 10 nodes.
That was the notation. Now the interesting part. Assume that a huge pentacle is drawn on the ground, and on each of its nodes, we have a gun with which you can shoot another node that is exactly two hops away. For example, in the figure, you can shoot A from C or vice versa, but you cannot shoot B from either A or C. Once a node has been shot, you cannot use it to shoot at another node. The goal is to start from any node and to keep shooting (only one shot at a time) until only one of the nodes remains. Can it be done? If so, how would you do that?
Hint: The solution to this problem is based on a simple strategy. Can you prove or disprove that this strategy is the only way to solve this problem?
