Project Euler Forum

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!

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?

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.