Le Monde puzzle [#869]

An uninteresting Le Monde mathematical puzzle:

Solve the system of equations

• a+b+c=16,
• b+c+d=12,
• d+c+e=16,
• e+c+f=18,
• g+c+a=15

for 7 different integers 1≤a,…,g≤9.

Indeed, the final four equations determine d=a-4, e=b+4, f=a-2, g=b-1 as functions of a and b. While forcing 5≤a, 2≤b≤5, and  7≤a+b≤15. Hence, 5 possible values for a and 4 for b. Which makes 20 possible solutions for the system. However the fact that a,b,c,d,e,f,g are all different reduces considerably the possibilities. For instance, b must be less than a-4. The elimination of impossible cases leads in the end to consider b=a-5 and b=a-7. And eventually to a=8, b=3… Not so uninteresting then. A variant of Sudoku, with open questions like what is the collection of the possible values of the five sums, i.e. of the values with one and only one existing solution? Are there cases where four equations only suffice to determine a,b,c,d,e,f,g?

Apart from this integer programming exercise, a few items of relevance in this Le Monde Science & Medicine leaflet.  A description of the day of a social sciences worker in front of a computer, in connection with a sociology (or sociometry) blog and a conference on Big Data in sociology at Collège de France. A tribune by the physicist Marco on data sharing (and not-sharing) illustrated by an experiment on dark matter called Cogent. And then a long interview of Matthieu Ricard, who argues about the “scientifically proven impact of meditation”, a sad illustration of the ease with which religions permeate the scientific debate [or at least the science section of Le Monde] and mingle scientific terms with religious concepts (e.g., the fusion term of “contemplative sciences”). [As another “of those coincidences”, on the same day I read this leaflet, Matthieu Ricard was the topic of one question on a radio quizz.]