  We study the statistical mechanics of a model glassy system based on a
familiar and popular mathematical puzzle. Sudoku puzzles provide a very rare
example of a class of frustrated systems with a unique groundstate without
symmetry. Here, the puzzle is recast as thermodynamic system where the number
of violated rules defines the energy. We use Monte Carlo simulation to show
that the "Sudoku Hamiltonian" exhibits two transitions as a function of
temperature, a paramagnetic and a glass transition. Of these, the intermediate
condensed phase is the only one which visits the ground state (i.e. it solves
the puzzle, though this is not the purpose of the study). Both transitions are
associated with an entropy change, paramagnetism measured from the dynamics of
the Monte Carlo run, showing a peak in specific heat, while the residual glass
entropy is determined by finding multiple instances of the glass by repeated
annealing. There are relatively few such simple models for frustrated or glassy
systems which exhibit both ordering and glass transitions, sudoku puzzles are
unique for the ease with which they can be obtained with the proof of the
existence of a unique ground state via the satisfiability of all constraints.
Simulations suggest that in the glass phase there is an increase in information
entropy with lowering temperature. In fact, we have shown that sudoku have the
type of rugged energy landscape with multiple minima which typifies glasses in
many physical systems, and this puzzling result is a manifestation of the
paradox of the residual glass entropy. These readily-available puzzles can now
be used as solvable model Hamiltonian systems for studying the glass
transition.
