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?

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) (Show Source): You can put this solution on YOUR website!

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

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
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