Since the 19th century, the teachers who are allowed to teach in the last years of High School in France are selected through a national contest called Agrégation. The written part consists of two problems (one in algebra, one in analysis) and the contestants have six hours to cope with each of them, on two consecutive days. The analysis problem of the year 2011 was based on a joint work by Nigel Kalton and Gilles Godefroy (Studia Mathematica, Vol. 159 (2003), 121-141) which was accessible through a quite elementary approach . The rule is that the authors of the Agrégation problems remain anonymous.