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Number Theory Level 5

If the number of digits in 9876543210 ! 9876543210! is n n , find the number of digits of n ! n! .

Notation : ! ! denotes the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .


The answer is 995290403109.

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Atul Shivam by Atul Shivam , 23, India

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1 solution

We just need to use stirling's approximation n ! ∼ 2 π n ( n e ) n n! \sim \sqrt{2\pi n} \left( \frac{n}{e}\right)^n and log tables.

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