#2             82. TRUE AND FALSE             

Tonya is sitting a true-false test consisting of five questions.

She knows that there are always more ‘true’ questions than ‘false’ questions, and that there are never more than two questions in a row with the same answer.

From the nature of the first and last questions, she knows that these have opposite answers.

She is greatly relieved to discover that she knows the answer to the second question – and not just because this means she has one answer right!

Why is this? And can you score full marks for the test?
HINT 1

You will have to test cases. Try first putting T for question 2 and build in the other information.
HINT 2

You will have found that some cases give several possibilities for test answers. Perhaps you can discard these cases?
SOLUTION

Suppose the answer to Question 2 if T. Then T, T, F, T, F and T, T, F, T, T both satisfy the conditions. Hence the answer to Question 2 is F. If the answer to Question 1 is also F, the conditions do not allow for any solution. Hence the answer to Question 1 is T, and the unique solution is T, F, T, T, F.
EXTENSION

Try creating your own True-False problem by making up a set of conditions to be satisfied. Remember though that you are looking for a problem set which has a unique solution.