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Le Monde puzzle [#887quater]

November 28, 2014

And 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, 2014

Here 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, 2014

As 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, 2014

A 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 […]

Le Monde puzzle [#882]

October 14, 2014

A terrific Le Monde mathematical puzzle: All integers between 1 and n² are written in an (n,n)  matrix under the constraint that two consecutive integers are adjacent (i.e. 15 and 13 are two of the four neighbours of 14). What is the maximal value for the sum of the diagonal of this matrix? Indeed, when considering […]

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