IR-MO 1997 Problem 6

Let $\mathcal P$ be the set of all points in $\mathbb R^n$ with rational coordinates. For the points $A,B \in \mathcal l{P}$ , one can move from $A$ to $B$ if the distance $AB$ is $1$ . Prove that every point in $\mathcal l{ P}$ can be reached from any other point in $\mathcal{P}$ by a finite sequence of moves if and only if $n \geq 5$ .