One of my teachers gives his students essay finals. First, he tells us three numbers, A, B, and C. He gives us A essay questions to study before the test. He picks B essay questions to put on the test, and we must pick out C of them to answer. He tells us to study A-B+C of the given questions if we want to pass the final.

As a procrastinator, I only studied the night before. Luckily, some other students had taken the test a day early, and could tell me which of the questions the teacher had picked. Of course, the teacher would pick a different combination of questions to give to the rest of the students. After hearing which questions were given, I realized I needed to study N less questions than was necessary before!

Find N, generalizing to all possible A, B, and C.

The answer is 1 for all A,B,C such that A>B>C>0

All we learn from the early testers is the exact set of problems the instructor will not repeat on the second version of the test. This means that we know that at least one of the questions on your test will be from the group not selected for the first testing group (there are A-B questions in this group).  Since we would have otherwise studied A-B+C questions, we simply study all A-B of the problems in the excluded group (knowing we have studied at least one of the final questions), then study C-1 of the previously included questions and we are covered

 If the teacher had told the students that the problems were selected at random for each testing group (allowing the possible but unlikely event of indentical tests) this would be fair for everyone.

Edited on April 8, 2005, 11:53 pm

Edited on April 8, 2005, 11:53 pm

Posted by Eric on 2005-04-08 23:52:46