# October Problem of the Month!

Congratulations to the winner of the September Problem of the Month: Thomas Morgan!

Now onto October’s:

Steven’s Self-improvement SSS

You need to start thinking about jobs, but your mother is worried that you’re not good at talking about yourself.  Fortunately, she hears about Steven’s Self-Referential Aptitude Program in the OU Math Department.   Unfortunately, it’s not what she thinks it is.  Not knowing this, she makes you go see Steven to fill out an application.  He gives you the following anti-entrance exam:  if you can’t solve it correctly, you have to go through his program.

Self-Referential Aptitude Quiz

For each of the following questions, the answer is the number of a question.

1. The answer to this question is the average of the answers to all of the questions.
2. This answer to this question is the number of a question whose answer is maximal.
3. The answer to this question is greater than the answer to any subsequent questions.
4. The answer to this question is a question number whose answer is the number of this question.
5. The answer to this question is not the answer to any other question.

Bonus.  Determine all solutions to Steven’s Quiz.

[See the rules in the PHSC 2nd floor display case for more information.]