A combinatoric Le Monde mathematical puzzle that resembles many earlier ones: Given a pool of 30 interns allocated to three person night-shifts, is it possible to see 31 consecutive nights such that (a) all the shifts differ and (b) there are no pair of shifts with a single common intern? In fact, the constraint there […]

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## Le Monde puzzle [#937]

November 11, 2015## Le Monde puzzle [#934]

October 25, 2015Another Le Monde mathematical puzzle with no R code: Given a collection of 2€ coins and 5€ bills that sum up to 120€, find the number of 5€ bills such that the collection cannot be divided into 5 even parts. Indeed, as soon as one starts formalising the problem, it falls apart: if there are […]

## Le Monde puzzle [#932]

October 15, 2015A Sudoku-like Le Monde mathematical puzzle: A 12×8 grid contains the first 96 integers, as in R matrix(1:96,ncol=12). If one picks 24 of those integers including 3 for each row and 2 for each column, what are the extreme values of the sum of the selected integers? I obviously rephrased quite strongly the question (and […]

## Le Monde puzzle [#930]

October 9, 2015A game Le Monde mathematical puzzle: On a linear board of length 17, Alice and Bob set alternatively red and blue tokens. Two tokens of the same colour cannot sit next to one another. Devise a winning strategy for the first player. In the ‘Og tradition, this calls for a recurrent R code: While I […]

## Le Monde puzzle [#929]

September 29, 2015A combinatorics Le Monde mathematical puzzle: In the set {1,…,12}, numbers adjacent to i are called friends of i. How many distinct subsets of size 5 can be chosen under the constraint that each number in the subset has at least a friend with him? In a brute force approach, I tried a quintuple loop […]