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We study the statistical mechanics of a model glassy system based on afamiliar and popular mathematical puzzle. Sudoku puzzles provide a very rareexample of a class of frustrated systems with a unique groundstate withoutsymmetry. Here, the puzzle is recast as thermodynamic system where the numberof violated rules defines the energy. We use Monte Carlo simulation to showthat the "Sudoku Hamiltonian" exhibits two transitions as a function oftemperature, a paramagnetic and a glass transition. Of these, the intermediatecondensed phase is the only one which visits the ground state (i.e. it solvesthe puzzle, though this is not the purpose of the study). Both transitions areassociated with an entropy change, paramagnetism measured from the dynamics ofthe Monte Carlo run, showing a peak in specific heat, while the residual glassentropy is determined by finding multiple instances of the glass by repeatedannealing. There are relatively few such simple models for frustrated or glassysystems which exhibit both ordering and glass transitions, sudoku puzzles areunique for the ease with which they can be obtained with the proof of theexistence of a unique ground state via the satisfiability of all constraints.Simulations suggest that in the glass phase there is an increase in informationentropy with lowering temperature. In fact, we have shown that sudoku have thetype of rugged energy landscape with multiple minima which typifies glasses inmany physical systems, and this puzzling result is a manifestation of theparadox of the residual glass entropy. These readily-available puzzles can nowbe used as solvable model Hamiltonian systems for studying the glasstransition.

The paramagnetic and glass transitions in sudoku