Question

a) In a collection of 900 coins, one is counterfeit and weighs either more or less than the genuine coins. Find a good lower bound on the number of balance scale weighings needed to identify the fake coin and determine whether it is too heavy or too light. Assume the balance scale has three states: tilted left, tilted right, or balanced.

b)In a collection of 10 coins, 2 coins are counterfeit and weigh less than the genuine coins. Find a good lower bound on the number of balance scale weighings needed to identify all the fake coins. (Assume the balance scale has three states: tilted left, tilted right, or balanced. )

c)Consider the problem of identifying a counterfeit coin with a balance scale. Suppose, as we did in Example 5.18, that 1 coin out of a set of 10 is fake, but this time suppose that the fake coin could be eithertoo heavy or too light, and it must be determined which is the case. What does Theorem 5.1 say about the minimum number of weighings in this case?

d)Suppose that one coin in a set of fourteen coins is fake, and that the fake coin is lighter than the other coins.

Use Theorem 5.1 to find a lower bound on the number of balance-scale weighings needed to identify the fake.

Answer 1

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