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MR1409378 (97h:11114) 11P21
Kolountzakis, Mihail N. A problem of Steinhaus: can all placements of a planar set contain exactly one lattice point? Analytic number theory, Vol. 2 (Allerton Park, IL, 1995), 559--565, Progr. Math., 139, Birkhäuser Boston, Boston, MA, 1996.
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