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Le Monde puzzle [#1012]

June 14, 2017

A basic geometric Le Monde mathematical puzzle: Take a triangle ABC such that the side AB is c=42 long, each side has an integer length, and the area is 756. Given an inner point D, draw three lines parallel to the three sides of ABC through D in order to construct three triangles with common […]

Le Monde puzzle [#1011]

June 9, 2017

An combinatoric Le Monde mathematical puzzle (with two independent parts): Given the following grid, What is the longest path from A to B that does not use the same edge twice?  What is the probability that two minimal length paths from A to B [of length 13] share the same middle [7th] edge? The first […]

Le Monde puzzle [#1010]

June 2, 2017

An arithmetic Le Monde mathematical puzzle (or two independent ones, again!): Take the integers from 1 to 19, pick two of them with identical parity at random and replace the pair with their average. Repeat 17 times to obtain a single integer. What are the values between 1 and 19 that cannot be achieved?  Take […]

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 […]