Professor Diogenes has n supposedly identical integrated-circuit chips that in prin- ciple are capable of testing each other. The professor's test jig accommodates two chips at a time. When the jig is loaded, each chip tests the other and reports whether it is good or bad. A good chip always reports accurately whether the other chip is good or bad, but the professor cannot trust the answer of a bad chip. Thus, the four possible outcomes of a test are as follows: Chip A says Chip B says Conclusion B is good A is good both are good, or both are bad B is good A is bad at least one is bad B is bad A is good at least one is bad B is bad A is bad at least one is bad b. Consider the problem of finding a single good chip from among n chips, as- suming that more than n/2 of the chips are good. Show that [n/2] pairwise tests are sufficient to reduce the problem to one of nearly half the size