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Within the transport model IBUU04, we investigate the double neutron/proton ratio of free nucleons taken from two reaction systems using two Sn isotopes at a beam energy of 50 MeV/nucleon and with impact parameters 2fro, 4fro and 8fm, respectively. It is found that the double neutron/proton ratio from peripheral collisions is more sensitive to the density dependence of the symmetry energy than those from mid-central and central collisions.