There are a bunch of puzzles I've encountered of the following form: You're given an undirected (finite) graph G, and a list of words. The problem is to label the vertices of the graph G with letters so that each of the words can be "spelled out" by following a path in the graph. The specific versions of this puzzle are the following: The list of words is the names of the nine (before Pluto got demoted) planets. The graphs are "rectangle graphs" -- i.e. an (m,n) rectangle graph has vertices labeled by (i,j) for 1 <= i <= m, 1 <= j <= n. Two vertices (i,j) and (i',j') are adjacent if you can transform one to the other by choosing one coordinate and adding or subtracting 1 -- i.e. Manhattan distance 1. The challenges are for the (5,7) and (4,8) rectangle graphs with the above words. A bigger challenge is to prove that you *can't* do it for the (5,6) graph. I know of no reasonable proof for the impossibility for the (5,6) graph other than running some intelligent exhaustive program for a long time (over 1 day). Can anyone do better? Victor