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The number 132 is a three digit number with three distinct digits that is equal to the sum of all two digit numbers that are made up of its three digits:

What is the largest three digit number with this property?

Incorrect

In the sum on the right, each digit appears twice in the tens column and twice in the units column. So if the digits are and we have

If this equation becomes , but this has no solutions as the right-hand-side is at most (as and are both at most . If then the equation becomes . For values of between and , is a multiple of only when or , and only gives a value of that is between and (). So the largest values is .

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