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at most n true statements

Source: 2019 Dürer Math Competition Finals Day2 E3 https://artofproblemsolving.com/community/c1621835_2019_

January 5, 2022
combinatorics

Problem Statement

On a piece of paper we have 20192019 statements numbered from 11 to 20192019. The nthn^{th} statement is the following: "On this piece of paper there are at most nn true statements". How many of the statements are true?
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