19.6. In the institute, there are truth-lovers, who always tell the truth, and liars, who always lie. One day, each employee made two statements.

1) There are not even ten people in the institute who work more than I do.
2) At least a hundred people in the institute earn more than I do.

It is known that the workload of all employees is different, and so are their salaries. How many people work in the institute?
19.6. Answer: 110. From the first statement, for the truth-teller with the least workload, it follows that there are no more than 10 truth-tellers in the institute, and for the liar with the greatest workload, it follows that there are no fewer than 10 truth-tellers in the institute. From the second statement, for the truth-teller with the highest salary, it follows that there are no fewer than 100 liars in the institute, and for the liar with the lowest salary, it follows that there are no more than 100 liars in the institute. Thus, there are 10 truth-tellers and 100 liars working in the institute.