Problem 217
Balanced Numbers

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

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK