MathDB

Let

n

be a positive integer. Initially a few positive integers are written on the blackboard. On one move Igor chooses two numbers

a, b

of the same parity on the blackboard and writes

\frac{a+b} {2}

. After a few moves the numbers on the blackboard were exactly

1, 2, \ldots, n

. Find the smallest possible number of positive integers that were initially written on the blackboard.

Problem Statement