Question 56
$P_{1}, P_{2}, \ldots, P_{n}$ are points in the plane and $r_{1}, r_{2}, \ldots, r_{n}$ are real numbers such that the distance between $P_{i}$ and $P_{j}$ is $r_{i} + r_{j}$ (for $i$ not equal to $j$). Find the largest $n$ for which this is possible.