Ed Pegg Jr <ed@mathpuzzle.com> wrote on 8 Apr 2003:
Serhiy Grabarchuk sent me a problem involving matchstick snakes [...]
Did you know that the UnaBomber enjoyed playing with matches? Below is one of his problems. A Match Stick Problem, Mathematics Magazine, Jan-Feb 1971 p.41 http://links.jstor.org/sici?sici=0025-570X(197101)44:1<41:PAS> 787. Proposed by T. J. Kaczynski, Lombard, Illinois Suppose we have a supply of matches of unit length. Let there be given a square sheet of cardboard, n units on a side. Let the sheet be divided by lines into n^2 little squares. The problem is to place matches on the cardboard in such a way that: a) each match covers a side of one of the little squares, and b) each of the little squares has exactly two of its sides covered by matches. (Matches are not allowed to be placed on the edge of the cardboard.) For what values of n does the problem have a solution? Solutions: Richard A. Gibbs: invokes Pick's theorem Richard L. Breisch: solves m by n generalization Math. Mag v.44 #5 Nov-Dec 1971 p.294 http://links.jstor.org/sici?sici=0025-570X(197111)44:5<294:PAS> Thomas Wray: solves n-dim generalization (match -> n-1 dim cube) Math. Mag. v.45 #2 Mar-Apr 1972 p.110 http://links.jstor.org/sici?sici=0025-570X(197203)45:2<110:PAS> -Bill Dubuque