The Steinhaus tiling problem and the range of certain quadratic forms
  We give a short proof of the fact that there are no measurable subsets of Euclidean space (in dimension d > 2), which, no matter how translated and rotated, always contain exactly one integer lattice point. In dimension d=2 (the original Steinhaus problem) the question remains open. 
Mihail N. Kolountzakis and Michael Papadimitrakis