I just picked up a copy of The USSR Olympiad Problem Book, by D.O. Shklarsky, N.N. Chentzov, and I.M. Yaglom, and it looks delightful. The book’s foreword states that it is intended for high-school students, although outstanding middle-school students might also give it a go. Complete solutions are given, which are particularly detailed for the more difficult problems. Hints are also given. These features make it particularly good as a training guide for problem-solving; the fact that it is an inexpensive Dover edition also doesn’t hurt.
Problem 4(a) on Page 7 states:
We are given 80 coins of the same denomination; we know that one of them is counterfeit and that it is lighter than the others. Locate the counterfeit coin by using four weighings on a pan balance.
Problem 4(b) asks readers to generalize this problem if there are n coins instead of 80; that is, what is the minimum number of weighings needed in general?
See if you can solve either problem, if you are interested, and I’ll post a solution in a few days.