Question 67
There are $n$ numbers on a blackboard. The following operation is performed on these numbers: two numbers $a$ and $b$ are erased and then the number $\frac{a+b}{4}$ is written. The operation is repeated $n-1$ times. As a result, a single number remains on the board. Prove that if all the original numbers are equal to 1, then the resulting number is not less than $1 / n$.