Summary: This study examines the relation between the Grundy numbers of a Maximum Nim and the Josephus problem. Let \(f(x) =\lfloor \frac{x}{k} \rfloor\), where \(\lfloor \rfloor\) is a floor function and \(k\) is a \(k\) positive integer such that \(k \geq 2\). We prove that there is a simple relation between a Maximum Nim with the rule function \(f\) and the Josephus problem, in which every \(k\)-th number is to be removed from \((1,2,3, \dots, n)\) for some natural number \(n\). Based on this relation, we propose a new method for solving the Josephus problem.