Abstract
This note deals with fair division problems; in particular, with cake-cutting procedures that result in an envy-free division. Despite intense eorts in the last decades, it seems that it is still an open question whether there is a nite bounded envy-free cake-cutting procedure for n players with n > 3.
However, quite recently, some authors have claimed to have solved the problem both for four players and for any nite number of players. The purpose of this note is to discuss recent work in this area and to point out several errors and confusion about some assumptions.