Chapter 5.1, Problem 30E

1. Given an equal arm balance capable of determining only the relative weights of two quantities and eight coins, all of equal weight except possible one that is lighter, explain how to determine if there is a light coin and how to identify it in just two weighings.

2. Given an equal arm balance as in (a) and $3^n-1$ coins, $n\ge 1$, all of equal weight except possibly one that is lighter, show how to determine if there is a light coin and how to identify it in at most $n$ weighings.