Art of Problem Solving: 2012 AMC 10 B #24 / AMC 12 B #16

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  • Опубліковано 25 жов 2024

КОМЕНТАРІ • 14

  • @arnavnarula1534
    @arnavnarula1534 7 років тому +4

    I found another solution. None of the people can like 4 songs, because they must dislike at least one song that the other two pairs like and none of the people can like 1 song, because they must like at least one song that the other two pairs like. This leaves 4 possible outcomes for the number of songs that people like: (3, 3, 3) , (3, 3, 2) , (3, 2, 2) , and (2, 2, 2). You can prove there are no options where all 3 people like 3 songs using some quick checking. Then, you can just count the possibilities for the 3 other options which are 36, 72, and 24 respectively. 36 + 72 + 24 = 108 + 24 = 132 possibilities.

  • @mr.orca3251
    @mr.orca3251 6 років тому +5

    10b 24 = 12b 16 apparently

    • @ryancao2408
      @ryancao2408 3 роки тому

      This is a tough question, so it's included in the harder section for the 9/10th graders.

    • @name-np4gr
      @name-np4gr 2 роки тому

      @@ryancao2408 im in 8th grade doing it lawl

    • @RaZorasiangamer
      @RaZorasiangamer Рік тому

      @@name-np4gr there’s a 6th grader in my school that got a 145.5 on this years A… he got a 60 smth on the B tho 🥱🥱🥱

    • @name-np4gr
      @name-np4gr Рік тому

      @@RaZorasiangamer wat

  • @rogerwang21
    @rogerwang21 4 роки тому +1

    671 and 1105 just seem like random answer choices pulled out of a hat in comparison to 108 and 132

  • @srikanthtupurani6316
    @srikanthtupurani6316 6 років тому

    this is amazing. there are some matching problems in graph theory which are too tough. they can be really frustrating.

  • @wisdomofwealth593
    @wisdomofwealth593 5 років тому +3

    You made a mistake around 2:00 you accidentally drew the same pair of girls twice

    • @AyushArt
      @AyushArt 4 роки тому

      ooh i was about to comment that too lol. (it was at 1:36)

  • @livedandletdie
    @livedandletdie 12 років тому +1

    stopped at 3:21 and the answer is simple. As each pair can like only one song together then there are 3 pairs that have 4 possible outcomes each and as each pair has their own choice there is 3*4^3 outcomes 64*3 192 then as they can't all like the same song there is 3*4^2 negative outcomes so 48 so 144 and then one takes the number of non-existing outcomes so 144-(3*4^1)=132. Not that hard. Why is de Bruijn sequence so useful. oh and First.

  • @sighmaniacrotmg6530
    @sighmaniacrotmg6530 6 років тому

    This is a pretty easy #24