MHB Calculating Median in a Class with B, D, A, and C Scores: Findings and Solutions

[Monoxdifly]

In a class, Budi's score is greater than Doni's. The sum of Adi's and Doni's scores is greater than the sum of Budi's and Coki's scores. Meanwhile, Doni's score is greater than two times Budi's score substracted by Adi's score. Determine the median of those four students' scores.

All I know, was, by using their initials that:
B > D
A + D > B + C
D > 2B - A

And by using the second and third info I got that their score from lowest to highest is either C, D, B, A or D, B, C, A. However, I met a dead-end after that. Please someone help me.

 

[skeeter]

I sketched a number line ... $B>D$ is obvious. The last inequality states $B < \dfrac{A+D}{2}$, or $B$ is less than the average of $A$ and $D$, equal to the midpoint of segment $AD$.

Finally, the second inequality states $C < A+D-B$. Note the possible positions for $C$ represented by the open-ended blue ray in the diagram.

If $B < C< A$ or $D < C < B$, the the median of the four scores is $\dfrac{B+C}{2}$

If $C < D$, then the median is $\dfrac{B+D}{2}$

 

[I like Serena]

Yep. Put more concisely, the median is $\frac 12 (B+\max(C,D))$.

 

[Monoxdifly]

Thank you everyone who has helped me with this question. I have asked this question in 4 different forums including this one and all confirm that it is impossible to find the exact number of the median's value.