Problem

Source: Stars of Mathematics - Seniors - Problem 4

Tags: graph theory, combinatorics proposed, combinatorics



Given $n$ sets $A_i$, with $| A_i | = n$, prove they may be indexed $A_i = \{a_{i,j} \mid j=1,2,\ldots,n \}$, in such way that the sets $B_j = \{a_{i,j} \mid i=1,2,\ldots,n \}$, $1\leq j\leq n$, also have $| B_j | = n$. (Anonymous)