  Finite geometry is used to underpin finite, $d^2$, dimensional Hilbert space
accommodating two particles, d dimensional each. d=prime $\ne2$. Central role
is allotted to states with mutual unbiased bases (MUB) labelling underpinned
with points of finite dual affine plane geometry (DAPG). The DAPG lines are
shown to underpin maximally entangled states which form an orthonormal basis
spanning the space and provide a novel, geometrical view to a new solution of
the Mean King Problem (MKP). Brief expositions to the topics considered: MUB,
DAPG and the MKP are included rendering the paper self contained.
