points: 5
level: Medium
title: Problem 7
author: Abhay Rana nemo@sdslabs.co.in
answer: e043d3b98a12e4af1819c18c326e7935a3a5b583
###Definitions
Define $f(x)$ as the sum of the factorials of the digits of x. For example, $$f(342) = 3! + 4! + 2! = 32$$
Define $sf(x)$ as the sum of the digits of $f(x)$. So $$sf(342) = 3 + 2 = 5$$
Define $g(i)$ to be the smallest positive integer $n$ such that $sf(n) = i$. Though $sf(342)$ is 5, $sf(25)$ is also 5, and it can be verified that $g(5)$ is 25
Define $sg(i)$ as the sum of the digits of $g(i)$. So $$sg(5) = 2 + 5 = 7$$
Further, it can be verified that $g(10)$ is 16 and sum of all $sg(i)$ for $1 \le i \le 10$ is 46
###Question
What is sum of all $sg(i)$ for $31 \le i \le 45$ ?