53. (6) In a line, numbers $1,2, \ldots, n$ are written in some order. A pair of numbers is called a pit if these numbers are adjacent, or there are only numbers between them that are smaller than each of them. What is the maximum number of pits? (A number can be part of several pits.)
$\square$ Answer: $2 n-3$.

In each cell, draw an arrow from the smaller number to the larger one. Notice that from each number $k$, two arrows cannot point in the same direction: the number at the end of the shorter one would be less than $k$. Therefore, from the numbers $1, 2, \ldots, n-2$, no more than 2 arrows can point outwards, and from the number $n-1$, no more than 1 arrow can point outwards, totaling no more than $2 n-3$. This is achievable: place 1 in the middle, and add the numbers $2, 3, \ldots, n$ in order at the edges, strictly alternating the edges.

(A. Lebedev, A. Shapovalov)