  We propose a mechanism for solving the `negative sign problem'---the
inability to assign non-negative weights to quantum Monte Carlo
configurations---for a toy model consisting of a frustrated triplet of
spin-$1/2$ particles interacting antiferromagnetically. The introduced
technique is based on the systematic grouping of the weights of the recently
developed off-diagonal series expansion of the canonical partition function
[Phys. Rev. E 96, 063309 (2017)]. We show that while the examined model is
easily diagonalizable, the sign problem it encounters can nonetheless be very
pronounced, and we offer a systematic mechanism to resolve it. We discuss the
generalization of the suggested scheme and the steps required to extend it to
more general and larger spin models.
