11 teams

[aras82]

A total of 11 teams participated in a tournament in which every team played exactly one match with every other team. In any match a team gets four points for a win, three points for a draw and two points for a loss. The total score of no two teams was the same at the end of the tournament. If the number of points of the team with the highest total score is 35 , then which could be the number of points of the team with the least total score ?

[Ramesss]

Originally Posted by aras82

A total of 11 teams participated in a tournament in which every team played exactly one match with every other team. In any match a team gets four points for a win, three points for a draw and two points for a loss. The total score of no two teams was the same at the end of the tournament. If the number of points of the team with the highest total score is 35 , then which could be the number of points of the team with the least total score ?

There must be typo error in question. Because, no. of matches each team played= n(n+1)/2=55
If any team scores 2 in every match total score(110) will be above the highest total score of 35.

[aras82]

am afraid, the question is correct.

[touche]

Matches are 55
if a team losses all matches it could get 20 points, if the ratio of wins and losses or draws fits in. The top team must have won 7, drew 1 and lost 2.

confused how to work out the ratios, a quick estimate gives me a guess fig of 25!