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Thread: I don't know how to describe this problem

  1. #1
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    Question I don't know how to describe this problem

    4 friends were singing at the concert. Each song was performed by 3 of them. Person A performed the most --> 10 songs, person B performed the least --> 8 songs. In total, how many songs did friends perform?
    Answers: 1) 8; 2) 12; 3) 10; 4) 11.

    I've been thinking for some time but I've got no idea how to tackle this problem. Describe your thought process while solving, please.
    Last edited by topsquark; Jun 14th 2019 at 06:52 PM.
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  2. #2
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    Re: I don't know how to describe this problem

    Quote Originally Posted by Jotaro View Post
    4 friends were singing at the concert. Each song was performed by 3 of them. Person A performed the most --> 10 songs, person B performed the least --> 8 songs. In total, how many songs did friends perform?
    Answers: 1) 8; 2) 12; 3) 10; 4) 11.

    I've been thinking for some time but I've got no idea how to tackle this problem. Describe your thought process while solving, please.
    #1 - Throw out 8. "A" sang 10. It can't be 8.
    #2 - What did "C" and "D" sing? "Least" and "Most" imply no ties. Otherwise, superlatives don't work. "C" and "D" must have sung how many songs?

    Are we getting anywhere?
    Last edited by topsquark; Jun 14th 2019 at 06:52 PM.
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  3. #3
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    Re: I don't know how to describe this problem

    Quote Originally Posted by Jotaro View Post
    4 friends were singing at the concert. Each song was performed by 3 of them. Person A performed the most --> 10 songs, person B performed the least --> 8 songs. In total, how many songs did friends perform?
    Answers: 1) 8; 2) 12; 3) 10; 4) 11.

    I've been thinking for some time but I've got no idea how to tackle this problem. Describe your thought process while solving, please.
    Here is my solution:
    $\dbinom{4}{3}=4$ Four choose three is four. So there are four groups of three.

    $ABC\quad 3\\ABD\quad 3\\ACD\quad 4\\BCD\quad 2$

    Now I leave to you to see that the above meets all requirements.

    I did that a Venn diagram on four sets.
    Last edited by topsquark; Jun 14th 2019 at 06:53 PM.
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  4. #4
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    Re: I don't know how to describe this problem

    I don't know how to describe this problem-songs.png

    $\displaystyle 3n=10+8+9+9$
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