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Problem 3 -- Whiteboard Wipeout

Source: 46th Austrian Mathematical Olympiad Regional Competition Problem 3

July 14, 2018
Austrianumber theory

Problem Statement

Let n≥3n \ge 3 be a fixed integer. The numbers 1,2,3,⋯ ,n1,2,3, \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)
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