  The mathematical structure of the widely popular Sudoku puzzles is akin to
typical hard constraint satisfaction problems that lie at the heart of many
applications, including protein folding and the general problem of finding the
ground state of a glassy spin system. Via an exact mapping of Sudoku into a
deterministic, continuous-time dynamical system, here we show that the
difficulty of Sudoku translates into transient chaotic behavior exhibited by
the dynamical system. In particular, we show that the escape rate $\kappa$, an
invariant characteristic of transient chaos, provides a single scalar measure
of the puzzle's hardness, which correlates well with human difficulty level
ratings. Accordingly, $\eta = -\log_{10}{\kappa}$ can be used to define a
"Richter"-type scale for puzzle hardness, with easy puzzles falling in the
range $0 < \eta \leq 1$, medium ones within $1 < \eta \leq 2$, hard in $2 <
\eta \leq 3$ and ultra-hard with $\eta > 3$. To our best knowledge, there are
no known puzzles with $\eta > 4$.
