Pick a Number, 1 to 20 by BruceM

Read the description (again) and then come back. Now just give any integer between 1 and 20 inclusive. Note that this is the only question where the full set of correct answers is knowable in advance. On questions 2-12 the correct answer(s) will turn out to be some subset of this question's correct answers.

How many players will NOT give a correct answer to question 1? For purposes of this question, an answer of 1 signifies "1 or fewer"; an answer of 20 signifies "20 or more."

If the sum of the valid answers to this question is odd then all valid odd answers will be correct; if the sum of the valid answers to this question is even then all valid even answers will be correct. For all questions on this quiz, "valid" answers any of the 20 possible answers listed in the directions. (In calculating sums, averages, etc., if N players give the same number as their valid answer then that number will be accounted for N times.)

If at least half of the players who take this quiz money this question then valid answers 11-20 will be correct; if fewer than half of the players who take this quiz money this question then valid answers 1-10 will be correct.

The most common valid answer to this question, and only the most common, will be marked correct.

The opposite direction from #5: you will be correct if and only if you give a valid answer that nobody else gives. (Note that if 39 or fewer players take this then at least one person is guaranteed to get this one right.)

Give a valid answer that comes within 1 of 2/3 the mean average of the valid answers to this question. (For example, if 3 players took this quiz and they gave 20, 20, and 5, then the mean would be 15, and so 2/3 of the mean would be 10, and so the answers 9, 10, and 11 would all be correct.)

If half or fewer of the valid answers are 8, then 8 will be the only correct answer. If more than half of the valid answers are 8, then 8 will be the only valid-but-incorrect answer.

Take the percent of players who got question 5 ("most common valid answer") right, divide by 5, and round up to the nearest integer. What will be the result? ("Percent" is a real number between 0 and 100.)

Take the percent of players who get THIS question right, divide by 5, and round up to the nearest integer. What will be the result? (Once again, "percent" is a real number between 0 and 100.)

What number am I thinking of?

Take the percent of players who money this question, divide by 5, and round up to the nearest integer. What will be the result? (Once again, "percent" is a real number between 0 and 100.)