Start of the season

Logic Level 3

In a standard league system (with 2 n 2n teams), each team has played one match after the first weekend.

Is it always true that the team in 1st place played the team in ( 2 n ) (2n) th place; the team in 2nd place played the team in ( 2 n 1 ) (2n-1) th place etc.?

Details and Assumptions:

  • The teams are ranked by the following criteria in this order, with the next criteria only being used, if teams are inseparable with the current criteria
  • Total points
  • Goal Difference
  • Goals For
  • If teams are still inseparable, they will be ordered such that the above question holds true
Yes No

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2 solutions

Zico Quintina
May 16, 2018

The statement is not always true because of the third criterion for ranking, Goals For. A simple counterexample would be the following: Team A beats Team X by a score of 4:3, while Team B beats Team Y by a score of 2:1. Neither of the first two criteria will separate Teams A & B, nor teams X & Y; then applying the third criterion, Team A would rank ahead of Team B, but Team X would rank ahead of Team Y.

Aaryan Vaishya
Jan 1, 2019

This is not always true because losing/winning does not always render a team worse/better than a team they have not played,the points is what matters.Say n is 50,there are 100 teams.The 1st place team scored 100 points and played against the second place team(who got 99).The third place team got 98,etc.This is an ultimate counter example as none of the teams played their 2n-x counterparts.So basically,the person who lost to the 1st place team could have been any position except 1st so the given in this problem is false.

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