AT-OEMO-REG 2015 Problem 3

Let $n \ge 3$ be a fixed integer. The numbers $1,2,3, \cdots , n$ 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.

(Theresia Eisenkölbl)