# Intriguing problem

Today, I , Svatejas and Vighnesh were chatting on slack and I accidentally came across this problem:

Find the largest integer $n$ such that $n! for some positive integer $a$ having $n$ digits.

Find a method to do this. Hoping for numerous approaches :)

Note by Nihar Mahajan
3 years, 6 months ago

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Here is an interesting result: $\lceil \log([\log(2^{10000})]!) \rceil = 9166$

- 3 years, 6 months ago

That was indeed surprising LOL

- 3 years, 6 months ago

@Nihar Mahajan Let's create some problem using factorials and 9166 tomorrow. Till then I won't follow anyone :P

- 3 years, 6 months ago

Sure!

- 3 years, 6 months ago

- 3 years, 6 months ago

There is no one-formula for this question.

- 3 years, 6 months ago

If we include some relation between $a$ and $n$ then? For example: if $a$ has $n$ digits.

- 3 years, 6 months ago

Then you can use Stirling's formula.

- 3 years, 6 months ago

I'll try to list all such integer till n=6 by tmmrw.(through coding obviously)

- 3 years, 6 months ago