For the first problem: I think your list of statements all look like this:

Statement # 1: There is exactly one false statement in this list.

Statement # 2: There are exactly two false statements in this list.

Statement # 3: There are exactly three false statements in this list.

.

.

.

Statement # 98: There are exactly 98 false statements in this list.

Statement # 99: There are exactly 99 false statements in this list.

Statement # 100: There are exactly 100 false statements in this list.

Obviously, at most one of these statements can be true, because they are all contradictory. You have two cases:

Case 1: None of the statements are true. Where does this lead?

Case 2: One of the statements is true. Where does this lead?