## Balanced Numbers

### Problem 217

Published on Friday, 14th November 2008, 09:00 pm; Solved by 831

A positive integer with k (decimal) digits is called balanced if its first k/2 digits sum to the same value as its last k/2 digits, where x, pronounced ceiling of x, is the smallest integer x, thus π = 4 and 5 = 5.

So, for example, all palindromes are balanced, as is 13722.

Let T(n) be the sum of all balanced numbers less than 10n.
Thus: T(1) = 45, T(2) = 540 and T(5) = 334795890.

Find T(47) mod 315