If you remember the previous post, I had two interpretations about Le Monde mathematical puzzle #639: Find all integers with less than 11 digits that are perfect squares and can be written as a(a+6), a being an integer. and: Find all integers with less than 11 digits that are perfect squares and can be written […]
A Le Monde mathematical puzzle about special integers: Find all integers with less than 11 digits that are perfect squares and can be written as a(a+6), a being an integer. Eleven digits being too much for a brute force exploration of the form `for (t in 1:1e11)`…, some preliminary analysis is needed, but I could […]
A combinatoric Le Monde mathematical puzzle that resembles many earlier ones: Given a pool of 30 interns allocated to three person night-shifts, is it possible to see 31 consecutive nights such that (a) all the shifts differ and (b) there are no pair of shifts with a single common intern? In fact, the constraint there […]
A combinatorics Le Monde mathematical puzzle: In the set {1,…,12}, numbers adjacent to i are called friends of i. How many distinct subsets of size 5 can be chosen under the constraint that each number in the subset has at least a friend with him? In a brute force approach, I tried a quintuple loop […]
A combinatorics Le Monde mathematical puzzle: In the set {1,…,12}, numbers adjacent to i are called friends of i. How many distinct subsets of size 5 can be chosen under the constraint that each number in the subset has at least a friend with him? In a brute force approach, I tried a quintuple loop […]
A combinatorics Le Monde mathematical puzzle: How many distinct integers between 0 and 16 can one pick so that all positive differences are distinct? If k is the number of distinct integers, the number of positive differences is 1+2+…+(k-1) = k(k-1)/2, which cannot exceed 16, because it is a subset of {1,2,…,16}, meaning k cannot […]
A combinatorics Le Monde mathematical puzzle: How many distinct integers between 0 and 16 can one pick so that all positive differences are distinct? If k is the number of distinct integers, the number of positive differences is 1+2+…+(k-1) = k(k-1)/2, which cannot exceed 16, because it is a subset of {1,2,…,16}, meaning k cannot […]
![Egyptian fractions [Le Monde puzzle #922]](https://i1.wp.com/idata.over-blog.com/1/30/67/45/Janvier-2012/gal3.jpg)
For its summer edition, Le Monde mathematical puzzle switched to a lighter version with immediate solution. This #922 considers Egyptian fractions which only have distinct denominators (meaning the numerator is always 1) and can be summed. This means 3/4 is represented as ½+¼. Each denominator only appears once. As I discovered when looking on line, […]
A puzzling Le Monde mathematical puzzle (or blame the heat wave): A pocket calculator with ten keys (0,1,…,9) starts with a random digit n between 0 and 9. A number on the screen can then be modified into another number by two rules: 1. pressing k changes the k-th digit v whenever it exists into […]
A truly terrible graph in Le Monde about overweight and obesity in the EU countries (and Switzerland). The circle presentation makes no logical sense. Countries are ordered by 2030 overweight percentages, which implies the order differs for men and women. (With a neat sexist differentiation between male and female figures.) The allocation of the (2010) […]
