SOLUTION: What is the sum of all 3-digit positive integers for which the multiplication of the sum of its digits and the product of its digits equals to the number itself?

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Question 1135441: What is the sum of all 3-digit positive integers for which the multiplication of the sum of its digits and the product of its digits equals to the number itself?
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The condition says that, given the 3-digit number ABC,

%28A%2BB%2BC%29%2A%28ABC%29+=+100A%2B10B%2BC

Very probably no algebraic solution is possible.

I used excel to find there are exactly two numbers that meet the requirements: 135 and 144.

ANSWER: 135+144 = 279