  The multiple-solution problem in determining the
three-interfering-resonances' parameters from a fit to an experimentally
measured distribution is considered in a mathematical viewpoint. In this paper
it is shown that there are four numerical solutions for the fit with three
coherent Breit-Wigner functions. Although the explicit analytical formulae can
not be derived in this case, we provide some constraint equations between the
four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner
forms of amplitude functions, numerical method is provided to derive the other
solutions from the already obtained one based on the obtained constraint
equations. In real experimental measurements with more complicated amplitude
forms similar to Breit-Wigner functions, the same method can be deduced and
performed to get numerical solutions. The well agreement between the solved
solutions using this mathematical method and those from the fit directly
verifies the correctness of the supplied constraint equations and mathematical
methodology.
