text: We show that for @math and for measurable subsets of the unit square with Lebesgue measure @math there exist bi-Lipschitz maps with bounded Lipschitz constant (uniformly over all such sets) which are identity on the boundary and increases the Lebesgue measure of the set to at least @math .
  @cite_5: A number of tricky problems in probability are discussed, having in common one or more infinite sequences of coin tosses, and a representation as a problem in dependent percolation. Three of these problems are of Winkler' type, that is, they ask about what can be achieved by a clairvoyant demon.
summary: The question considered in this paper has connections to several different problems in analysis, an interested reader is referred to @cite_5 and the references therein for more details.