FERMAT 2012 Problem 25

There are many positive integers N with the following properties:

  • the digits of N include at least one of each of the digits 3,4,5, and 6 ,
  • the digits of N include no digits other than 3,4,5, and 6 , and
  • the sum of the digits of N is 900 and the sum of the digits of 2 N is 900 .

When the largest and smallest possible values of N are multiplied together, the number of digits in the resulting product is

Answer Choices
A. 408
B. 400
C. 432
D. 416
E. 424