When a packing is found empirically, there is always the question of whether it is really exists.  Since the coordinates as numbers are always slightly in error, possibly the circles overlap, say by some tiny amount.  Possibly the system of equations is inconsistent, but just barely so.  If by numerical methods, a solution of the equations converges without difficulty we can be confident that a solution really exists.  We can be certain the packing exists if, in addition, the polynomial equations can be solved by algebraic means, or at least reduced to a univariate polynomial.  Sometimes this can be done, when n is sufficiently small, by Groebner basis methods or by using resultants with maple or other computer algebra system.

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