Given a matrix $A \in \{0,1\}^{n \times n}$, let $diag(A)$ be the set of vectors $D \in \{0,1\}^n$ that are a diagonal of the $n!$ matrices obtained from $A$ via row permutations.

What is the maximum size of $|diag(A)|$ over all matrices $A \in \{0,1\}^{n \times n}$?

Given a matrix $A \in \{0,1\}^{n \times n}$, let $diag(A)$ be the set of vectors $D \in \{0,1\}^n$ that are the diagonal of one of the $n!$ matrices obtained from $A$ via row permutations.

What is the maximum size of $|diag(A)|$ over all matrices $A \in \{0,1\}^{n \times n}$?

Given an n by $n$ matrix with $0$'s and $1$'s only, consider the $n!$ different permutations generated by permuting the rows, what is the maximum number of different diagonals generated?

Given a matrix $A \in \{0,1\}^{n \times n}$, let $diag(A)$ be the set of vectors $D \in \{0,1\}^n$ that are a diagonal of the $n!$ matrices obtained from $A$ via row permutations.

What is the maximum size of $|diag(A)|$ over all matrices $A \in \{0,1\}^{n \times n}$?