Challenge June-2019

Map Coloring with Violations                                                                     Solutions

This challenge is an advanced version of the May-2019 Challenge.  Previously you had 4 colors (blue, red, green, or yellow) but now you have only 3 colors (blue, red, green). It is not enough to color six European countries: Belgium, Denmark, France, Germany, Luxembourg, and the Netherlands in such a way that no neighboring countries use the same color. So, some neighboring counties may have the same colors but there is a relative cost for such violations:

France – Luxembourg: $257
Luxembourg – Germany: $904
Luxembourg – Belgium: $568

You need to find a solution that minimizes the total violation cost. Please submit your solutions to