# Tag: asymptotics

## asymptotics – Is there a function that grows faster than exponentially but slower than a factorial?

The Question : 123 people think this question is useful In big-O notation the complexity class $O(2^n)$ is named “exponential”. The complexity class $O(n!)$ is named “factorial”. I believe that $f(n) = O(2^n)$ and $g(n) = O(n!)$ means that $\dfrac{f(n)}{g(n)}$ goes to zero in the limit as $n$ goes to infinity. Is there any known

## combinatorics – How many fours are needed to represent numbers up to $N$?

The Question : 222 people think this question is useful The goal of the four fours puzzle is to represent each natural number using four copies of the digit $4$ and common mathematical symbols. For example, $165=\left(\sqrt{4} + \sqrt{\sqrt{{\sqrt{4^{4!}}}}}\right) \div .4$. If we remove the restriction on the number of fours, let $f(N)$ be the