PUZZLET 065

Repeated Digit Product

Multiplying the digits of an integer
together always produces a smaller number. If the new integer is
submitted to the same process, an even smaller number will
appear. Eventually, the resultant integer will be less than 10,
and no further reduction is possible. Example: 29 ---> 2 x 9 = 18 ---> 1 x 8 = 8, representing 2 iterations. What is the smallest integer that generates a single digit using this process within two iterations? 3, 4, 5, 6, and 7 iterations? |

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Last Updated: January 12th, 2010.