A game Le Monde mathematical puzzle: On a linear board of length 17, Alice and Bob set alternatively red and blue tokens. Two tokens of the same colour cannot sit next to one another. Devise a winning strategy for the first player. In the ‘Og tradition, this calls for a recurrent R code: While I […]

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## Le Monde puzzle [#930]

October 9, 2015## Le Monde puzzle [#929]

September 29, 2015A 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 […]

## Le Monde puzzle [#907]

September 18, 2015A combinatorics (?) Le Monde mathematical puzzle: Each day of 2014, more than half of the 365 Paris métro drivers are at work. What is the minimal number of drivers one should consider to be sure to include at least a driver for each day of the year? I may be missing an item of […]

## Le Monde puzzle [#928]

September 10, 2015A 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]

July 28, 2015For 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, […]