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Magic Pairs


The pair of numbers 3 and 37037 is "magic." Here is how the magic works: Pick your favorite digit from among 1, 2, 3, or 9, and multiply it by 3. Multiply the result by 37037. What is the final answer?

Is the pair of numbers 13 and 8547 "magic?" pick your favorite digit from among 1, 2, 3, or 9, and multiply it by 13. Multiply the result by 8547. What is the final answer?

How many pairs of "magic" numbers exist?

(Source: Mathematics Teaching in the Middle School, Sep 1998)



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