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## Discussion of Problem 1483. Table Football

Strange approach
Posted by andreyDagger 25 Feb 2022 22:50
It's obvious that answer for first team is n - 1

How to get answer for second team. Of course total number of points do not exceed
3 * (n * (n - 1) / 2), because we played n * (n - 1) / 2 matches, and in every match summary points not exceed 3. Assume looser team got k points, that mean that total number of points >= k * n. But k * n can't be greater than 3 * n * (n - 1) / 2, so:
k * n <= 3 * n * (n - 1) / 2, then k <= 3 * (n - 1) / 2.

Answer is 3 * (n - 1) / 2.
Re: Strange approach
Posted by Apkawa 8 Jun 2022 21:18
But how to prove that we can make such competition where k is the smallest value and we have (n - 1) values that are not less?

Edited by author 08.06.2022 21:21