A very interesting question
is a card \(hash\)
We first take L about a few dozen to ensure that the result will exceed \(10^9 + 7\)
Then randomly output \(10^5\) characters
From the prompt of the title, we can think that if we have the number of \(n\) and choose \(k\) times, then the expected number of repeated numbers is:
\[\sum\limits_{i = 0}^{k } \frac{i}{n}\]
We make
\[\sum\limits_{i = 0}^{k} \frac{i}{n} = 1\]
to solve \(k\) approximately equal to \(\sqrt{n}\)
It can be proved that randomly select \(\sqrt{n}\) numbers in the range of \(n \) , and expect to have at least one repeated number