This puzzle is based off of Graph Theory research at the University of Arizona Department of Computer Science and elsewhere. The Threshold Coloring Problem is concerned with a graph G=(V,E), whose edges have each been labeled Near or Far. The goal is to assign integer colors to each vertex, so that if two vertices share an edge then the difference in their colors is greater than some threshold t if and only if the shared edge has been labeled far. The first threshold coloring paper can be found at arxiv.