The Principle of Inclusion and Exclusion: Problem 3

Problem: There are 60 students standing in a line, facing their teacher. Each of them are labeled 1, 2, 3, all the way to 60. The teacher first instructs all the students whose label is a multiple of four to turn 180 degrees. Then, she instructs all the students whose label is a multiple of five to turn 180 degrees. Finally, she instructs all the students whose label is a multiple of 6 to turn 180 degrees. How many students are facing the teacher?

Key: Create the correct Venn diagram

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