There are four pirates splitting treasury. During the night, each pirate comes and discovers the treasury has $4n+1$ many golds. So they take $n+1$ and leave the remaining $3n = 4k+1$ for some other pirates. After the night, the four pirates come and again realize there are $4n+1$ golds for some $n$. So they each take $n$ and leave $1$ dollar as operation cost. What is the smallest possible number of golds initially.
Writing some code shows that it's $1021$. I wonder if there is some easy solution to this brain teaser. What I observed in calculation: the possible number for the initial treasury are $1024n - 3$ and $1024 = 2^8$. This is not a trivial pattern, so there might be some easy rational that I just don't see.
Let the original pieces of gold be $4n_0+1$. For $i = 1, 2, 3, 4$, let the pieces of gold left, after the looting of pirate $i$ during the night, be $4n_i+1$.
So we have $3 n_i = 4 n_{i+1} + 1$, or $3 (n_i+1) = 4 (n_{i+1} + 1)$. Therefore, $n_0+1 = 3^{-4} 4^4 (n_4+1)$. The minimum value of $n_4$ to maintain all integer $n_i$ is thus $n_4 + 1 = 3^4$.
The rest is then obvious.