## Le Monde puzzle [#1164]

November 16, 2020

The weekly puzzle from Le Monde is quite similar to older Diophantine episodes (I find myself impossible to point out): Give the maximum integer that cannot be written as 105x+30y+14z. Same question for 105x+70y+42z+30w. These are indeed Diophantine equations and the existence of a solution is linked with Bézout’s Lemma. Take the first equation. Since […]

## Le Monde puzzle [#1158]

November 10, 2020

A weekly puzzle from Le Monde on umbrella sharing: Four friends, Antsa, Cyprien, Domoina and Fy, are leaving school to return to their common housing. It is raining and they only have one umbrella with only room for two. Given walking times, x¹, x², x³ and x⁴, find the fastest time by which all of […]

## Le Monde puzzle [#1159]

October 6, 2020

The weekly puzzle from Le Monde is quite similar to #1157: Is it possible to break the ten first integers, 1,…,10, into two groups such that the sum over the first group is equal to the product over the second? Is it possible that the second group is of cardinal 4? of cardinal 3? An […]

## Le Monde puzzle [#1157]

October 1, 2020

The weekly puzzle from Le Monde is an empty (?) challenge: Kimmernaq and Aputsiaq play a game where Kimmernaq picks ten different integers between 1 and 100, and Aputsiaq must find a partition of these integers into two groups with identical sums. Who is winning? Indeed, if the sums are equal, then the sum of […]

## Le Monde puzzle [#1155]

September 26, 2020

The weekly puzzle from Le Monde is another Sudoku challenge: Anahera and Wiremu play a game for T rounds. They successively pick a digit between 1 and 3, never repeating the previous one, and sum these digits. The last to play wins if the sum is a multiple of 3. Who is the winner for […]