  The paper examines a trapped one-dimensional system of multicomponent
spinless fermions that interact with a zero-range two-body potential. We show
that when the repulsion between particles is very large the system can be
approached analytically. To illustrate this analytical approach we consider a
simple system of three distinguishable particles, which can be addressed
experimentally. For this system we show that for infinite repulsion the energy
spectrum is sixfold degenerate. We also show that this degeneracy is partially
lifted for finitely large repulsion for which we find and describe
corresponding wave functions.
