Fundamental Solution for this Problem Solving Question

This question appeared in my math/ problem solving competition. It goes like this : Six competitors in a chess tournament played against each other once only. (That totals fifteen games). A win is worth one point, a draw is worth half a point and a loss is worth no points. The fourth player scored 2 points and the sixth player scored 1 point. There were no equal scores, while the person who came first had no losses and one draw. Work out the second players score.

I have figured out that the 5th person must have had 1 and a half points and also know that the second person must have in between 3 and 4 points. However, I cannot proceed from here and would like to appeal to someone for their insight on how to solve such problems.

P.S I do not know what to tag this post. If someone could help it would be greatly appreciated.

• So you know the number of points won by positions 1,4,5,6.... how many points are left to allocate to the remaining 2 players? – Joffan Jul 23 '18 at 6:52
• 15-4.5-2-1.5-1=6 – Boris KR Jul 23 '18 at 6:57

so $x+y=15-9=6$
the only possibility involving no equal scores is $x=3.5; y=2.5$