Teams	Played	Wins	Losses	Draws	Points
A	5	3	0	2	8
B	5	3	2	0	6
C	5	2	2	1	5
D	5	1	1	3	5
E	5		1
F	5

From the given points, we can figure out from A to D how their matches went, i.e. how many they won, lost, or ended with a draw.

Teams	Played	Wins	Losses	Draws	Points
A	5	3	0	2	8
B	5	3	2	0	6
C	5	2	2	1	5
D	5	1	1	3	5
E	5	0	1	4	4
F	5

We know that E and F have less than 5 points each. It's given that E has one loss, so now he has 4 more matches. All 4 of these have to be draws, because that's the only case where E will have less than 5 points. Even a single win would exceed the points and contradict what's given.

Teams	Played	Wins	Losses	Draws	Points
A	5	3	0	2	8
B	5	3	2	0	6
C	5	2	2	1	5
D	5	1	1	3	5
E	5	0	1	4	4
F	5	0	3	2	2

Things to note: Total Number of Points $=30$, since there will be a total of $15$ matches and each match results in two points (if a team loses, the winning team gets two points and if a match ends in a draw, both teams get one point each) Hence, $E+F=6$ points $F=2$ points F could have either 1 win, 4 losses, 0 draws or 0 wins, 3 losses, and 2 draws. The table becomes inconsistent with the former, since no two teams can have 0 draws and B already has 0 draws. Hence, the table above is our table. From it, we can see that F scored 2 points.

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