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.
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.
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.
10b 24 = 12b 16 apparently
This is a tough question, so it's included in the harder section for the 9/10th graders.
@@ryancao2408 im in 8th grade doing it lawl
@@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 🥱🥱🥱
@@RaZorasiangamer wat
671 and 1105 just seem like random answer choices pulled out of a hat in comparison to 108 and 132
this is amazing. there are some matching problems in graph theory which are too tough. they can be really frustrating.
You made a mistake around 2:00 you accidentally drew the same pair of girls twice
ooh i was about to comment that too lol. (it was at 1:36)
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.
oh and.... no one asked
This is a pretty easy #24
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