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Question 17

The digit sum of any number is the sum of its digits. $$N$$ is a three digit number. When the digit sum of $$N$$ is subtracted from $$N$$, we obtain the square of the digit sum of $$N$$. The number $$N$$ is


Correct Answer: 156

Solution

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Let the digit sum of $$N$$ be $$s$$. Then $$N-s=s^2$$, so $$N=s^2+s$$. Checking possible digit sums up to $$27$$ gives $$s=12$$, which produces $$N=12^2+12=156$$. The digit sum of $$156$$ is indeed $$12$$, verifying the answer.

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