The approximation technique called multi state Monte Carlo optimization (MSMCO) is employed here to estimate the solution to a six hundred point travelling salesman problem of finding the shortest route to connect the points in a closed loop. The six hundred points chosen for this solution attempt are a composite of several well known 100-point problems (with proven exact optimals) taken from the literature. This affords some comparison of the performance of the MSMCO approach with other techniques as many algorithms have been tried in producing the true optimals to the separate 100-point subproblems. An effort to show the versatility of the MSMCO technique is made by also attempting to solve a non-linear system with 60 variables and 15 equations. Real valued variables are used in the problem although integer, complex or mixed variable values could be used as the application required.