| Surprise Maximization (1999) | |
Abstract | |
| Surprise Maximization Borwein Borwein and Mar echal July The Surprise Examination Unexpected Hanging Paradox has long fascinated mathematicians and philosophers the number publications devoted attests For exhaustive bibliography the subject the reader referred Herein the optimization problems arising from information theoretic avoidance the Paradox are examined and solved They provide very satisfactory application both the Kuhn Tucker theory and various classical inequalities and estimation techniques Although the necessary convex analytic concepts are recalled the course the paper some elementary knowledge optimization assumed Readers unfamiliar with this background may simply skip couple proofs and few technical details information measure surprise The Paradox formulated Timothy Chow these pages A teacher announces class that examination will held some day during the following week and moreover that the examination will surprise The students argue that surprise exam cannot occur For suppose the exam were the last day the week Then the previous night the students would able predict that the exam would occur the following day and the exam would not surprise impossible for surprise exam occur the last day But then surprise exam cannot occur the penultimate day either for that case the students knowing that the last day impossible day for surprise exam would able predict the night before the exam that the exam would occur the following day Similarly the students argue that surp | |
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