This is Greg's revised solution. Colors help to identify distance between any two points. All Light Blue are one edge from Blue, and thus at most two edges from another Light Blue. All Pink are one edge from Red, and thus at most two edges from another Pink. All Green are one edge from both Red and Blue, and thus at most two edges from another Green, a Light Blue or a Pink. Because Blue and Red are one edge apart then all Colors are at most three edges apart. Since the one White is only two edges from Red and Blue it is at most three edges from all Colors.

Greg hopes that this graph minimizes or comes close to minimizing the sum of the number of edges between all point pairs, but is not mathematically- or time-endowed enough to prove it.





This is Greg's original solution to Dr. Dobb's Laser Shuttle Puzzle: