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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?

 May 21, 2020
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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.

 
 May 21, 2020
edited by Guest  May 21, 2020

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