Quote (Ricelol @ May 12 2012 03:57am)
We don't know, because infinity/infinity = indeterminate. It'spossible that you could pass by only answering 7.
Actually that's not true. The number of questions for which 7 is the answer divided by the number of questions for which the answer is any other real number can be calculated as follows:
(Note that while the size of the sets can't be calculated exactly, the quotient can still be found by writing the size of the 2nd in terms of the size of the first)
For any x in R (real numbers) let R(x) denote the set of questions for which x is the answer.
Then observe that for any other real number y, R(x) = R(y) - (y-x) (ie for any question in R(y), if you alter the question by subtracting (y-x) from it, you get x as the answer instead and thus it must now be a question in R(x)) The same works in the opposite direction, so we have a 1-1 correspondence between questions in R(x) and R(y). Thus |R(x)| = |R(y)| (# of questions for which x is the answer is the same as the # of questions for which y is the answer for all real numbers x and y)
Thus it follows simply that the number of questions for which 7 is the answer divided by the number of questions for which the answer is any other real number is |R(7)| / sum(|R(x)|, x is any real number except 7) = |R(7)| / sum(|R(7)|, x is any real number except 7) = 1 / |R ~ {7}| = 0
Therefore, the number of questions for which 7 is the answer is negligible compared to the number of questions for which the answer is any other real number, and the quotient is 0.