The Surprise Examination or Unexpected Hanging Paradox has long fascinatedmathematicians and philosophers, as the number of publications devotedto it attests.
In this talk, the optimization problems arising from an information theoreticavoidance of the Paradox are examined and solved. They provide a very satisfactoryapplication of both the Kuhn-Tucker theory (or dynamic programming) and of variousclassical inequalities and estimation techniques. Although the necessary convexanalytic concepts are recalled in the course of the talk, some elementary knowledgeof optimization is assumed. Those unfamiliar with this background may simply ignorea couple of proofs and few technical details.
This is joint work with D. Borwein (UWO) and P. Marechal (CECM and Montpellier). Our joint paper is:D. Borwein, J.M. Borwein and P. Marechal, "Surprise maximization,"American Math. Monthly, 107, June-July 2000, 527-537.It is also available at http://www.cecm.sfu.ca/preprints/1998pp.html, as CECMpreprint 98:116.