On a piece of paper, we can read the following 100 statements:

1. On this piece of paper, exactly one statement is false. 2. On this piece of paper, exactly two statements are false.
2. On this piece of paper, exactly three statements are false. .
3. On this piece of paper, exactly 100 statements are false.

Determine which statements are true on the paper.
Among the statements on the paper, any two contradict each other, so at most one statement can be true. The 100th statement cannot be true, because otherwise it would contradict itself. If the 100th statement is false, then there is a true statement among the statements, so according to our previous remark, there is exactly one true statement, and the other 99 are false. It is precisely this fact that the 99th statement records, so among the statements on the paper, the 99th statement is true, and the rest are false.