Question 62
A positive integer is called "balanced" if it has four digits, and one of these digits is equal to the average of the other three. For example: the number $2631$ is balanced because $3$ is the average of $2, 6$ and $1$; $4444$ is also balanced because $4$ is the average of $4, 4$ and $4$.
a) Find the three smallest balanced numbers.
b) How many balanced numbers are smaller than $2014$?
a) Find the three smallest balanced numbers.
b) How many balanced numbers are smaller than $2014$?