Hint
The fourth player is the key to this tricky question.
Answer
9 points.
Respectively the scores were 7, 14, 20, 30, 23, 9.
Reasoning
If we label the six players A, B, C, D, E, and F, we know that:
[1] A + B + C + D + E + F = 103
and from the clues:
A = B ÷ 2 B = C − 6 C = D x 2 ÷ 3 E = D − A F = E − 14
Note that it could be E = A − D or E = D − A, but using A − D we'd end up with a negative value for E later, which isn't allowed (so we'd have to try again with D − A anyway).
As we have no information for D, it's best to find all of the other letters in terms of D. These steps are left as an exercise (e.g. use C in the equation for B), but the result is:
A = ( D − 9) ÷ 3 B = (2D − 18) ÷ 3 C = (2D ) ÷ 3 D = (3D ) ÷ 3 E = (2D + 9) ÷ 3 F = (2D − 33) ÷ 3
Writing it as D = 3D ÷ 3 makes things slightly clearer in the next step.
Answer
Here are the contents of the containers after each stage:
A = 9 litres, B = 4 litres
A B
9 0 fill A
5 4 fill B from A (leaving 5 litres in A)
5 0 empty B
1 4 fill B from A (leaving 1 litre in A)
1 0 empty B
0 1 fill B from A
9 1 fill A
6 4 fill B from A (only 3 more litres fit in B)
6 0 empty B