Le Monde puzzle [#1078]

Recalling Le Monde mathematical puzzle  first competition problem

Given yay/nay answers to the three following questions about the integer 13≤n≤1300 (i) is the integer n less than 500? (ii) is n a perfect square? (iii) is n a perfect cube?  n cannot be determined, but it is certain that any answer to the fourth question (iv) are all digits of n distinct? allows to identify n. What is n if the answer provided for (ii) was false.

When looking at perfect squares less than 1300 (33) and perfect cubes less than 1300 (8), there exists one single common integer less than 500 (64) and one single above (729). Hence, it is not possible that answers to (ii) and (iii) are both positive, since the final (iv) would then be unnecessary. If the answer to (ii) is negative and the answer to (iii) is positive, it would mean that the value of n is either 512 or 10³ depending on the answer to (i), excluding numbers below 500 since there is no unicity even after (iv). When switching to a positive answer to (ii), this produces 729 as the puzzle solution.

Incidentally, while Amic, Robin, and I finished among the 25 ex-aequos of the competition, none of us reached the subsidiary maximal number of points to become the overall winner. It may be that I will attend the reward ceremony at Musée des Arts et Métiers next Sunday.

Compstat 2010

As a member of the scientific committe of the incoming Compstat 2010 meeting, taking place in Paris next August (22-27), I have received abstracts to evaluate. The abstracts were available through EasyChair and I have never seen the like of this system! It looks as if it was conceived in the final months of the former DDR…  All abstracts come into a single bland page with no access to abstracts before papers are selected. Once I have made my selection of papers I would like to review, the list of selected papers still does not provide the abstracts. A true nightmare…

Note that the meeting will be held in the beautiful buildings of the  Conservatoire National des Arts et des Métiers,  which is also linked with Umberto Eco’s Foucault’s Pendulum since it partly takes place there. Another point of relevance is that Jean-Michel Marin will give a tutorial on Bayesian Core during Compstat 2010. (He will focus on Bayes factor approximations.)