SOLUTION: If the 3 digit positive integer n = ABC = AB + BA + AC + CA + BC + CB, compute the largest possible value for n. (Note: A, B, C are single digits from 0 to 9)

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Question 356934: If the 3 digit positive integer n = ABC = AB + BA + AC + CA + BC + CB, compute the largest possible value for n. (Note: A, B, C are single digits from 0 to 9)
Answer by robertb(4012) About Me  (Show Source):
You can put this solution on YOUR website!
The values of A, B, C are guided by the equation 26A+-+4B+-+7C+=+0. We only need to consider i) odd values for B and even values for C, and
ii) even values for B and even values for C.
Only 3 ordered triples (A, B, C)will satisfy the constraint equation above:
(2,6,4), (1,3,2), and (3,9, 6). Therefore the largest n is 396.