A Question From The USSR Olympiad Problem Book

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.

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About Santo D'Agostino

I have taught mathematics and physics since the mid 1980s. I have also been a textbook writer/editor since then. Currently I am working independently on a number of writing and education projects while teaching physics at my local university. I love math and physics, and love teaching and writing about them. My blog also discusses education, science, environment, etc. https://qedinsight.wordpress.com Further resources, and online tutoring, can be found at my other site http://www.qedinfinity.com
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