# Find the Maximum Value of k

Question

We are given 2014 positive numbers such that

x(1) < x(2) < x(3) <… < x(2014)

It is known that the number x(k) is 19 times the average of the 2014 numbers.

(a) Determine the maximum possible value of k

(b) Give an example of 2014 numbers

x(1) < x(2) < x(3) <… < x(2014) such that this maximum value is achieved

A Possible Solution

(Please refer to the attached images)