Three distinct digits a, b, c are used to form six different three-digit numbers. What is the greatest positive integer that is a divisor of the sum of those six numbers, regardless of the original numbers chosen?

Guest May 21, 2020

#1**0 **

Example: a=1, b=5, c=8

[158, 185, 518, 581, 815, 851]=3,108

No matter what digits you use, when you permute them in 6 different permutations and sum them up, you always will get a number that is a multiple of 37.

**Therefore, 37 is the greatest positive divisor.**

Guest May 21, 2020

edited by
Guest
May 21, 2020