A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advan- tageous to guess among the rest?

If no answer choices are eliminated, the expected value for guessing is:

This is less than the value for leaving it unanswered, so we need to eliminate something. Suppose we were able to eliminate one answer and then guess:

Eliminating one more choice:

The minimum number of choices we would need to eliminate is 2.