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Le Monde puzzle [#1009]

May 26, 2017

An incomprehensible (and again double) Le Monde mathematical puzzle (despite requests to the authors! The details in brackets are mine.): A [non-circular] chain of 63 papers clips can be broken into sub-chains by freeing one clip [from both neighbours] at a time. At a given stage, considering the set of the lengths of these sub-chains, […]

Le Monde puzzle [#1008]

May 16, 2017

An arithmetic Le Monde mathematical puzzle (or two independent ones, rather): The set of integers between 1 and 2341 is partitioned into sets such that a given set never contains both n and 3n. What is the largest possible size of one of these sets?  Numbers between 1 and 2N are separated in two sets […]

Le Monde puzzle [#1006]

May 3, 2017

Once the pseudo-story [noise] removed, a linear programming Le Monde mathematical puzzle: For the integer linear programming problem max 2x¹+2x²+x³+…+x¹⁰ under the constraints x¹>x²+x³, x²>x³+x⁴, …, x⁹>x¹⁰+x¹, x¹⁰>x¹+x² find a solution with the maximal number of positive entries. Expressed this way, it becomes quite straightforward to solve with the help of a linear programming R […]

Le Monde puzzle [#1003]

April 18, 2017

A purely arithmetic Le Monde mathematical puzzle: Find the four integers w, x, y, z such that the four smallest pairwise sums among the six pairwise sums are 59, 65, 66, and 69. Similarly, find the four smallest of the five integers v, x, y, z such that the five smallest pairwise sums among the […]

Le Monde puzzle [#1002]

April 4, 2017

For once and only because it is part of this competition, a geometric Le Monde mathematical puzzle: Given both diagonals of lengths p=105 and q=116, what is the parallelogram with the largest area? and when the perimeter is furthermore constrained to be L=290? This made me jump right away to the quadrilateral page on Wikipedia, […]