  Matt Blum conjectured that the number of tilings of the Hexagonal Dungeon of
sides $a,\ 2a,\ b,\ a,\ 2a,\ b$ (where $b\geq 2a$) is
$13^{2a^2}14^{\lfloor\frac{a^2}{2}\rfloor}$ (J. Propp, New Perspectives in
Geometric Combinatorics, Cambridge University Press, 1999). In this paper we
present a proof for this conjecture using Kuo's Graphical Condensation Theorem
(E. Kuo, Applications of Graphical Condensation for Enumerating Matchings and
Tilings, Theoretical Computer Science, 2004).
