A journalist from Lokalbladet visits a school class with 25 students, and asks, among other things
about which clubs they belong to. In his office, he looks through the results:
• 11 students belong to the swimming club.
• 13 students belong to the football club.
• 10 students belong to the dance club.
But 11 + 13 + 10 will be more than 25! he thinks, and calls the school because it doesn't seem right. Many are members of more than one club, the teacher says. The journalist sends out a question paper and finds out that
• 6 students belong to both the football club and the swimming club.
• 7 pupils belong to both the football club and the dance club.
• 5 students belong to both the swimming club and the dance club.
• 5 students do not belong to any of the clubs.
When he gets the paper back he realizes that he should also have asked how many people are in all three clubs. Since he doesn't want to call the school again, he decides to try to figure it out.
1. How many of the students belong to all three clubs?
2. How many of them are in just one club?
Sorry for such a long text, please help!
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Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows the Pythagorean theorem. It was probably the first number known to be irrational.[citation needed]
The sequence A002193 in the OEIS consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places:
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