For a set of five true or false statements, no student in a class has written all correct answers and no two students in the class have written the same sequence of answers.What is the maximum number of students in the class, for this to be possible.

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Solution

For a set of true/false questions, the number of different answers produced would be $2 \times 2 \times 2 \times 2 \times 2 = 32.$ (Since for every question there can be two possible answers)
Out of these 32 combinations, only 1 set is correct.
Since, no one gave the correct answer and no two students gave the same set of answers, there are 31 such students.

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