  In any infinite dimensional Hilbert space $\mathcal H$ there exist orthogonal
projections $Q_1$, $Q_2$ and $Q_3$, such that a sequence $(P_n... P_1(x))$
diverges in norm for some $P_1,P_2,...\in\{Q_1,Q_2,Q_3\}$ and $x\in\mathcal H$.
