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 […]

## Search Results

## Le Monde puzzle [#887quater]

November 28, 2014## 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 […]

## Le Monde puzzle [#882]

October 14, 2014A 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 […]