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Problem of the Day #393: A Number Game April 15, 2012

Posted by Saketh in : potd , trackback

Scott is playing with numbers. To begin, he selects any four-digit number (leading zeros are allowed).

Each turn, he sorts the digits of his current number in both ascending and descending order to produce two other values. He then subtracts the smaller of these from the larger, and keeps the result as his new number.

Eventually, Scott’s routine reaches the fixed point $6174$. We call it a fixed point because $7641 – 1467$ simply produces $6174$ again. How many possible values are there for his starting number?

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