An arithmetics Le Monde mathematical puzzle: For which n’s are the averages of the first n squared integers integers? Among those, which ones are perfect squares? An easy R code, for instance which produces 333 values which are made of all odd integers that are not multiple of 3. (I could have guessed the exclusion […]

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## Le Monde puzzle [#899]

February 8, 2015## Le Monde puzzle [#887quater]

November 28, 2014And yet another resolution of this combinatorics Le Monde mathematical puzzle: that puzzle puzzled many more people than usual! This solution is by Marco F, using a travelling salesman representation and existing TSP software. N is a golden number if the sequence {1,2,…,N} can be reordered so that the sum of any consecutive pair is a […]

## Le Monde puzzle [#887ter]

November 27, 2014Here is a graph solution to the recent combinatorics Le Monde mathematical puzzle, proposed by John Shonder: N is a golden number if the sequence {1,2,…,N} can be reordered so that the sum of any consecutive pair is a perfect square. What are the golden numbers between 1 and 25? Consider an undirected graph GN […]

## Le Monde puzzle [#887bis]

November 16, 2014As mentioned in the previous post, an alternative consists in finding the permutation of {1,…,N} by “adding” squares left and right until the permutation is complete or no solution is available. While this sounds like the dual of the initial solution, it brings a considerable improvement in computing time, as shown below. I thus redefined […]

## Le Monde puzzle [#887]

November 15, 2014A simple combinatorics Le Monde mathematical puzzle: N is a golden number if the sequence {1,2,…,N} can be reordered so that the sum of any consecutive pair is a perfect square. What are the golden numbers between 1 and 25? Indeed, from an R programming point of view, all I have to do is to […]