Titu Andreescu and Zuming Feng have provided a new installment in the USA and International Mathematical Olympiads series, this time covering 2001. The book contains three sets of problems: the USAMO (USA Mathematical Olympiad) problems, the problems from the test used to select the US team for the International Olympiad, and the IMO (International Mathematical Olympiad) problems. For each set of problems, the authors provide first hints, then formal solutions.
These problems are elementary but not easy. Consider the very first one:
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. Determine, with justification, the smallest integer n for which this is possible.
The hint for this problem just says "the answer is not 24". Can you solve it?
Fernando Q. Gouvêa (firstname.lastname@example.org) is the editor of FOCUS and MAA Online.