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To this nice inequality my attention was called byE. Makai.
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Tóth, L.F. On the sum of distances determined by a pointset. Acta Mathematica Academiae Scientiarum Hungaricae 7, 397–401 (1956). https://doi.org/10.1007/BF02020534
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DOI: https://doi.org/10.1007/BF02020534