  Let $G=(V,E)$ be an undirected graph without loops and multiple edges. A
subset $C\subseteq V$ is called \emph{identifying} if for every vertex $x\in V$
the intersection of $C$ and the closed neighbourhood of $x$ is nonempty, and
these intersections are different for different vertices $x$.
  Let $k$ be a positive integer. We will consider graphs where \emph{every}
$k$-subset is identifying. We prove that for every $k>1$ the maximal order of
such a graph is at most $2k-2.$ Constructions attaining the maximal order are
given for infinitely many values of $k.$
  The corresponding problem of $k$-subsets identifying any at most $\ell$
vertices is considered as well.
