Just found this math puzzle online:

> 
> Original puzzle: Using one zero (and no other numbers) and
>  mathematical (including trigonometric and advanced) operations, how
>  can you achieve a final result of 6?
> 
> 
> Advanced one: Using only trigonometric functions and a single instance
>  of the number zero, derive a forumula to calculate any positive
>  integer n.
> 
> 
> 

I am sure there is an answer somewhere online but I can't find one - very interesting.

And the answer I can think of for the original one is

> 
> $$\lim\_{x\to0}\;(a^x+ a^x+ a^x+ a^x+ a^x+ a^x)$$
> 
> 
>