Question 1
Each of eight boxes contains six balls.
Each ball has been colored with one of $n$ colors,
such that no two balls in the same box are the same color,
and no two colors occur together in more than one box.
Find with proof the smallest possible $n$.
Each ball has been colored with one of $n$ colors,
such that no two balls in the same box are the same color,
and no two colors occur together in more than one box.
Find with proof the smallest possible $n$.