In my book it says: On the nth statement of a list of 100 statements, it says "There are exactly n number of false statements in this list."
It is said that this concludes that the 99th statement is true while the others are false.
But how does it tell that? n could be just any arbitary numbers, isn't it? If n=20, the 99th statement may not be true. Statements #5, #8, #34, and other random statements could be true but not the 99th one. Moreover, n could also be not 20 but 5, 50, or even 100. What should my thought process be when coming to this conclusion?
Then, it also says that if the nth statement becomes "At least n number of statements in this list are false."
It is said that statements 1 to 50 are true and 51 to 100 are false.
But again, how is this possible? n could again be any number, not neccessarily be right in the middle of the list of 100 statements. Even if it is n is 50, it is just 50 false statements in possibly different order. It does not need to be the first or last 50 of the list of statements.
Am I missing something that I don't understand how these conclusions were drawn?