Hello everyone,
Can you tell if my understanding of a successful agreement is correct?
Given that each of the friends have an order of preference which is a random permutation of [1, 2, 3, ..., n], which one of these is the logic for agreeing on an option?
- To agree on k, k must be the first (0th index) preference of at least 2 friends
- To agree on k, k must be the ith index preference of at least 2 friends
First logic one does not work for both P(3) and P(10) while the second does not work for P(10). It seems both logics are wrong, but I can't think of anything else from the problem's language!
Problem 906
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Don't start a new topic for a problem if there already exists one
See also the topics:
Don't post any spoilers
Comments, questions and clarifications about PE problems.
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brob26
- Administrator
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- Joined: Thu Nov 22, 2018 3:48 am
Re: Problem 906
We have made a slight adjustment to wording to hopefully clarify the clause. It now reads:
"They choose option $i$ if for every alternative option $j$ at least two of the three friends prefer $i$ over $j$."
In other words, to choose $i$, it is needed that for every other option $j$, $i$ appears before $j$ in at least two of the three orders of preference.
Does that help?
"They choose option $i$ if for every alternative option $j$ at least two of the three friends prefer $i$ over $j$."
In other words, to choose $i$, it is needed that for every other option $j$, $i$ appears before $j$ in at least two of the three orders of preference.
Does that help?
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raiden11
- Posts: 5
- Joined: Sat Aug 03, 2024 7:07 pm
Re: Problem 906
Understood it now. Thanks a lot!
This statement was helpful: In other words, to choose $i$, it is needed that for every other option $j$, $i$ appears before $j$ in at least two of the three orders of preference.
This statement was helpful: In other words, to choose $i$, it is needed that for every other option $j$, $i$ appears before $j$ in at least two of the three orders of preference.