Le Monde sans puzzle #933

While Le Monde mathematical puzzle is purely geometric this week

If twelve points in a plane are such that, for any 5-uplet of those, at least 4 are on the same circle, and if M is the largest number of those points on the same circle, what is the minimal value of M?

and not straightforward to solve with an R code, there are several entries of interest in the Sciences and Medicine leaflet. One about capture-mark-recapture: making fun of a PLOS One paper on a capture-recapture study about the movements of bed bugs in New Jersey apartments. Another one on the resolution by Terry Tao of Erdös’ discrepancy conjecture. Which states that. for any (deterministic) sequence f:N{1,+1} taking values in {1,+1}, the discrepancy of f is infinite, when the discrepancy is defined as

\sup_{n,d} \left|\sum_{j=1}^n f(jd)\right|

The entry in Le Monde tells the story of the derivation of the result and in particular the role of the Polymath5 project launched by Tao. It is interesting it is such a hard problem when considering the equivalent for a random sequence, which is more or less the gambler’s ruin result of Huygens. And a third entry on the explosion of the predatory journals, which publish essentially every submission in open access provided the authors accept to pay “charges”. And borrow titles and formats from existing reviews to a point where they can fool authors…

2 Responses to “Le Monde sans puzzle #933”

  1. The webpage is down and the page on Infinimath dates back to July 2014 so they do not seem to have continued this in the recent past. At least I could not find a link…

  2. Royi Avital Says:

    It seems your link to the dedicated page for those puzzles is broken.

    Could you update the link to the correct one?

    Thank You.

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