MathNet 2015-part-01 — 191 problems (EN–VI) Question 37

Let $n \ge 3$ be a fixed integer. The numbers $1, 2, 3, \dots, n$ are written on a board. In every move one chooses two numbers and replaces them by their arithmetic mean. This is done until only a single number remains on the board.
Determine the least integer that can be reached at the end by an appropriate sequence of moves.