  We solve a well known and long-standing open problem in database theory,
proving that Conjunctive Query Finite Determinacy Problem is undecidable. The
technique we use builds on the top of our Red Spider method which we developed
in our paper [GM15] to show undecidability of the same problem in the
"unrestricted case" -- when database instances are allowed to be infinite. We
also show a specific instance $Q_0$, ${\cal Q}= \{Q_1, Q_2, \ldots Q_k\}$ such
that the set $\cal Q$ of CQs does not determine CQ $Q_0$ but finitely
determines it. Finally, we claim that while $Q_0$ is finitely determined by
$\cal Q$, there is no FO-rewriting of $Q_0$, with respect to $\cal Q$, and we
outline a proof of this claim
