The Index and Length of Factorials

A factorial is an integer which is
the product of its index and all the integers less than its index.
Thus, factorial four (denoted 4!) is equal to 4 x 3 x 2 x 1 = 24. Find all factorials whose length (number of digits) equals their index. That is, those factorials in which n! contains n digits. To get you started, the first few factorials are shown in the table. |

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Last Updated: January 14th, 2010.