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5 teams play in a soccer competition

Source: Irish MO 2017 paper 2 problem 2

December 12, 2022
combinatorics

Problem Statement

55 teams play in a soccer competition where each team plays one match against each of the other four teams. A winning team gains 55 points and a losing team 00 points. For a 0−00-0 draw both teams gain 11 point, and for other draws (1−1,2−2,3−3,1-1,2-2,3-3,etc.) both teams gain 2 points. At the end of the competition, we write down the total points for each team, and we find that they form 5 consecutive integers. What is the minimum number of goals scored?
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