 The problem
is not intended to be solved by trial-and-error; there 
are deterministic methods for solving (x0,y0) 
in this case (see text).Numerous solutions starting as early as 1928 have been published both for the original problem and Williams modification.Clever and succinct solutions using modulo congruences, sieves, and alternate number bases have been devised based partly or mostly on the recursive definition of the problem, a structure that won't be applicable in the general case.