Le Monde puzzle [#852]

A number theory Le Monde mathematical puzzle:

Integers n of type A are such that the set {1,…,3n} can be written as the union of n sets of three integers of the form {a,b,a+b}. Integers n of type B are such that the set {1,…,3n} can be written as the union of n sets of three integers of the form {a,b,c} with a+b+c constant. What are the integers of type B? The smallest integer of both type A and type B is 1. What are the next two integers? Is it true that for n of type A, 4n and 4n+1 are of type A?

Again a case when writing a light R code proves out of (my) reach. When n grows, a brute-force search of all partitions quickly gets impossible. So no R solution provided here! (Feel free to suggest one.)

The Feb. 12, 2014, edition of the Sciences&Medicine leaflet is not that exciting either: mostly about medical topics. It however confirmed my solution for the #853 puzzle (44 and 42, esp.), with a tribune of Marco Zito who read the Edge 2014 annual question on What scientific idea is ready for retirement: he was [surprisingly] disappointed that those entries of a few thousand signs lacked validation and were mere speculations… (One of the entries was written by Nassim Taleb on standard deviation, which should be replaced with MAD, which Taleb mistakenly called mean absolute deviation, instead of median absolute deviation. Gerd Gireneizer has another (short) entry against the blind use of p-values, poorly titled as “Scientific Inference Via Statistical Rituals” as it sounds directed against the whole of statistics.) And then a short but interesting article on a large number of French universities cancelling their subscriptions to major journals like Science or Physical Review Letters. As they cannot follow the insane inflation in the prices of journals, thanks to the unrestricted greed of commercial editors (sounds like the Elsevier boycott did not have such an impact on the profession). The article contains this absurd quote from a Science editor who advances that all articles of the journal are freely available one year after their publication. One year is certainly better than two, ten or an infinity of years. Nonetheless, edge research is about what is published now rather than last year. A final mention for a tribune (in the Economics leaflet) complaining about the impact of the arrival of continental “scientific” business students and  mathematicians on the City, which deprived it from bright students from humanities and led to the financial crisis of 2008… Apparently, some are still looking for scapegoats!