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SMO 2005 Senior Round 2 Question 1

SMO · SMO 2005 Senior Round 2

Question 1

The digits of a 3-digit number are interchanged so that none of the digits retain their original positions. The difference of the two numbers is a 2-digit number and is a perfect square.

**Source clarification.** The printed statement ends here and omits an explicit request. Its accompanying solution identifies the possible differences. Under that intended interpretation, determine all possible positive differences and justify your answer. This clarification is editorial; the question remains marked for review.