15. Five Bunchkins sit in a horizontal field. No three of the Bunchkins are sitting in a straight line. Each Bunchkin knows the four distances between her and each of the others. Each Bunchkin calculates and then announces the total of these distances. These totals are $17,43,56,66$ and 76. A straight line is painted joining each pair of Bunchkins. What is the total length of paint required?
SOLUTION
129

Each line's length will be announced twice; once by each of the two Bunchkins at its ends. By adding up the total of the numbers announced we will therefore include the length of each line exactly twice.
The total length of paint required is $\frac{1}{2} \times(17+43+56+66+76)=\frac{258}{2}=129$.