GAUSS8 2018 Problem 24

Lynne chooses four distinct digits from 1 to 9 and arranges them to form the 24 possible four-digit numbers. These 24 numbers are added together giving the result N. For all possible choices of the four distinct digits, what is the largest sum of the distinct prime factors of N ?

Answer Choices
A. 157
B. 148
C. 127
D. 146
E. 124