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Principle of Inclusion and Exclusion

Count to 100. How many of those numbers are odd or multiples of 5? Since 50 are odd and 20 are multiples of 5, at first glance the answer is 70...

Principle of Inclusion and Exclusion: Level 1 Challenges


In a town of 50,000 people,
28,000 people read NanJing Morning News,
23,000 people read NanJing Evening News, and
4,000 people read both.

How many people read neither?

Katie is teaching a class of thirty pupils, of which fourteen are girls. She knows that there are twenty-two pupils who are right-handed.

What is the minimum number of girls who are right-handed in this class?

How many positive integers less than or equal to 60 are divisible by 3, 4 or 5?

At a construction site, Jorge is in charge of hiring skilled workers for the project. Out of 80 candidates that he interviewed, he found that

45 of them were painters;
50 of them were electricians ;
50 of them were plumbers;
15 of them had skills in all three areas;
all of them had skills in at least one of these areas.

If he hired everyone who were skilled in exactly 2 areas, how many candidates were hired?

For the integers from 1 to 1000, how many multiples of 9 are also multiples of 6?


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