medium Brainteasers

True Statement

A release-checked medium problem for training Brainteasers.

Question

On a sheet of paper, you have $100$ statements written down. The first statement says, "at most $0$ of these $100$ statements are true." The second says, "at most $1$ of these $100$ statements are true." More generally, the $n$th says, "at most $n-1$ of these $100$ statements are true. How many of the statements are true?

Practice focus

This Brainteasers problem is tagged Brainteasers. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.