Is the Post Office Metric applicable in $\Bbb{R}^n$ for all $n$? I was required to provide a metric space $(X,d)$ with $x,y\in X$ and $0<r<R$ such that $B_R(x)\subsetneq B_r(y)$. After a lot of thinking and reading, I came by a metric function called the "Post Office Metric", always attributed to $\Bbb{R}^2$, in particular when giving examples for a metric space such as the above. I constructed a metric function (defined on $\Bbb{R}$) of the same concept as follows: $d(x,y)=
\begin{cases}
|x|+|y|,  & \text{if } x\ne y \\
0, & \text{otherwise}
\end{cases}$, 
and to what I checked it seems like a legitimate metric function. Then I looked for it and came by nothing like that, and I begin to feel like I am doing something wrong. I would appreciate your thought on the matter.

UPDATE: Have fun with the standard interval $[0, 1]$! I think that's what the other answer did. (saw the picture of the graph answer and that idea popped up at the same time the third answer came)
What about something like $d(x, y)=||x||/2+||y||$? Should be pretty easy to come up with the values of $x, y$ and $0<r<R$...assuming you meant for all your parameters to be existential.
