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.
Digit 2 is smaller than Digit 4Digit 4 is two thirds of Digit 1Digit 1 is two thirds of Digit 3Digit 3 is three times Digit 2
By (3), Digit 3 is divisible by 3:
Digit 3 = 3, 6, 9
By (3), Digit 1 is two thirds of Digit 3:
Digit 1 = 2, 4, 6.
But, by (2), Digit 1 is divisible by 3:
Digit 1 = 6, and Digit 3 = 9.
By (4), Digit 3 is three times Digit 2:
Digit 2 = 3.
By (2), Digit 4 is two thirds of Digit 1:
Digit 4 = 4.
??
Puzzle 8
Can you find the number that best completes this puzzle?
