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# 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 $$n!<a$$ for some positive integer $$a$$ having $$n$$ digits.

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

Note by Nihar Mahajan
9 months, 2 weeks ago

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Here is an interesting result: $$\lceil \log([\log(2^{10000})]!) \rceil = 9166$$ · 9 months, 2 weeks ago

That was indeed surprising LOL · 9 months, 2 weeks ago

@Nihar Mahajan Let's create some problem using factorials and 9166 tomorrow. Till then I won't follow anyone :P · 9 months, 2 weeks ago

Sure! · 9 months, 2 weeks ago

I'll try to list all such integer till n=6 by tmmrw.(through coding obviously) · 9 months, 2 weeks ago

There is no one-formula for this question. · 9 months, 2 weeks ago

If we include some relation between $$a$$ and $$n$$ then? For example: if $$a$$ has $$n$$ digits. · 9 months, 2 weeks ago