Question 116
On a blackboard one wrote the numbers $1, 2, 3, \dots, 27$. One step consists in erasing three numbers $a, b, c$ from the blackboard and writing instead the number $a + b + c + n$, where $n$ is a fixed positive integer. Determine $n$ knowing that, after 13 steps, the number $n^2$ is written on the blackboard.