Question 13
For an $ n \times n $ matrix $ A $, let $ X_i $ be the set of entries in row $ i $, and $ Y_j $ the set of entries in column $ j $, $ 1 \leq i, j \leq n $. We say that $ A $ is golden if $ X_1, \ldots, X_n, Y_1, \ldots, Y_n $ are distinct sets. Find the least integer $ n $ such that there exists a $ 2004 \times 2004 $ golden matrix with entries in the set $ \{1, 2, \ldots, n\} $.