# Problem 217: Balanced Numbers

![graphic](img217.gif)

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