  We consider the one-dimensional quantum-statistical problem of interacting
spin-less particles in an infinite deep potential valley and on a ring. Several
limits for the applicability of the Quantum Monte Carlo (QMC) methods were
revealed and discussed. We show the inapplicability of the QMC method for
ring-like geometries, realize an unphysical frustration for interacting
fermions and a minus-sign problem for interacting bosons.
