## Le Monde puzzle [#845]

**Y**et another one of those Le Monde mathematical puzzles which wording is confusing to me:

Take the set of integers between 1 and 1000. endow all of them randomly with red or blue tags. group them by subsets of three or more (grapes). and also group them by pairs so that a switch can change the colour of both integers. Is it always possible to activate the switches so that one ends up with all grapes being multicoloured? Unicoloured?

**I** find it (again!) ultimately puzzling since there are configurations where it cannot work. In the first case, take a grape made of four integers of the same colour, reunited two by two by a switch: activating the switch simply invert the colours but the grape remains uni-coloured. Conversely, take two integers with opposite colours within the same grape. No mater how long one operates the switch, they will remain of an opposite colour, won’t they?!

**T**his issue of Le Monde Science&Médecine leaflet actually had several interesting entries, from one on *“the thirst of the sociologist for statistical irregularities*“—meaning that regression should account for confounding factors like social class versus school performances—to the above picture about weighting the mass of a neutrino—mostly because it strongly reminds of Escher, as I cannot understand the 3D structure of the picture—, to another tribune of Marco Zito informing me that “quark” is a word invented by James Joyce—and not by Carroll as I believed—, to an interview of Stanislas Dehaene, a neuroscientist professor at Collège de France and a (fairly young) member of the Académie des Sciences—where he mentions statistical learning patterns that reminded me of the Bayesian constructs Pierre Bessière discussed on France Culture—.

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