How to Play M 13?

A puzzle called “M ₁₃” J. H. Conway has described recently is explained. We report an implementation of the puzzle in the programming language Java. The program allows the human user to “play M ₁₃” interactively (and to cheat by solving it automatically). The program is an example on how to bring to life a nice piece of discrete mathematics. In this sense it presents not only a didactical way of seeing “mathematics at work”, but also displays the stabilizer chain method developed by C. Sims to solve group theoretic puzzles, the most famous of which being Rubik's cube.     

Structural studies on alkylisocyanate polymers by thermal degradation tandem mass spectrometry

Homopolymers and copolymers of alkylisocyanates having n-hexyl, 2,6-dimethylheptyl, 3,7-dimethyloctyl, and (2,2-dimethyl-1,3-dioxolan-4-yl)methyl substituents underwent thermal degradation in the course of desorption electron ionization to yield trimers and monomers that were characterized in situ by tandem mass spectrometry. The trimers were trisubstituted cyanuric acids, the protonated molecules displaying a characteristic series of alkene eliminations on collision-induced dissociation to yield protonated cyanuric acid, m/ z 130. Confirmation of the identity of the pyrolysates was obtained by using two types of MS3 experiments: the reaction intermediate scan and the two-dimensional familial scan. The ion chemistry of the trimers and of the protonated monomer, the alkylisocyanate, was elucidated. Among the many interesting fragmentation processes undergone by the ionized trimers were a and 3 C-C bond cleavages and charge-remote fragmentations, which provided information on branching in the alkyl substituent. The dioxolane-containing substituent showed unique ion chemistry. The monomer distribution in the copolymers was deduced from the abundances of the various protonated trimers. The distribution was found to be random in all copolymers except that containing the dioxolane substituent.