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UKMT Junior Kangaroo, 2015

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

Peter has a lock with a three-digit code. He knows that all the digits of his code are different and that if he divides the second digit by the third and then squares his answer, he will get the first digit. What is the difference between the largest and smallest possible codes?

(A) $42$ (B) $468$ (C) $499$ (D) $510$ (E) $541$

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