a) In a collection of 900 coins, one is counterfeit and weighseither more or less than the genuine coins. Find a good lower boundon the number of balance scale weighings needed to identify thefake coin and determine whether it is too heavy or too light.Assume the balance scale has three states: tilted left, tiltedright, or balanced.
b)In a collection of 10 coins, 2 coins are counterfeit and weighless than the genuine coins. Find a good lower bound on the numberof balance scale weighings needed to identify all the fake coins.(Assume the balance scale has three states: tilted left, tiltedright, or balanced. )
c)Consider the problem of identifying a counterfeit coin with abalance scale. Suppose, as we did in Example 5.18, that 1 coin outof a set of 10 is fake, but this time suppose that the fake coincould be eithertoo heavy or too light, and it must bedetermined which is the case. What does Theorem 5.1 say about theminimum number of weighings in this case?
d)Suppose that one coin in a set of fourteen coins is fake, andthat the fake coin is lighter than the other coins.
Use Theorem 5.1 to find a lower bound on the number ofbalance-scale weighings needed to identify the fake.
