R\'esolution du jeu de Juniper Green

TL;DR

This paper presents an elementary method to solve the Juniper Green game for all integers, reducing the problem to fewer than fifty cases that can be quickly solved with basic divisor and multiple concepts.

Contribution

It introduces a general approach to solve the Juniper Green game for almost all integers, simplifying the process to a manageable number of cases.

Findings

A universal solution method for the Juniper Green game.

Reduction of complex cases to fewer than fifty manageable ones.

Solutions can be obtained quickly with basic arithmetic techniques.

Abstract

In this article, we describe the solution of the Juniper Green game for every integer, with techniques that are elementary enough to be explained to students who have mastered the notions of divisors and multiples. A general method allows us to solve the game for almost every integer, then there are less than fifty cases left to deal with. Each of these cases can be solved within a few minutes, with a paper and a pencil. -- Dans cet article, nous d\'ecrivons la r\'esolution du jeu de Juniper Green pour tout entier, avec des techniques suffisamment \'el\'ementaires pour \^etre expliqu\'ees \`a des \'el\`eves ma\^itrisant les notions de diviseurs et multiples. Une m\'ethode g\'en\'erale permet de r\'esoudre le jeu pour presque tout entier, si bien qu'il reste alors moins de cinquante cas \`a traiter, chacun pouvant \^etre r\'esolu au prix d'une \'etude sur papier de quelques minutes.