Mr. Dolittle gave Glenda’s class a pop quiz. It had only five questions, all true-false. There's trouble: Glenda only knows the answer to one question, (#2). The rest she must guess. Is she in trouble? Not at all, for Mr. Dolittle is sadly predictable. Glenda knows:
- Mr. Dolittle’s quizzes always have more true answers than false,
- Mr. Dolittle doesn’t let three consecutive questions have the same answer,
- the first and last questions always have different answers.
Glenda aced the quiz without guessing a single answer. Given this information, what are the answers to the five questions?
Solution
We don’t know the answer Glenda had for question #2. If it was T, there are three possibilities consistent with Mr. Dolittle’s feeble quiz preparation rules. They are in the figure, part A. Glenda wouldn’t know which of these to use. She didn’t guess, so she must have known that questions #2 was false, for in this case there is only one possibility, as shown in the figure, part B. These must be the correct answers to the quiz.
