Question 23
Some overlapping circles divide the plane into several regions. Numbers are filled in these areas such that for any pair of overlapping circles, say A and B, the number in the intersection area of circle A and B is the average of the two numbers in the areas solely in A or B. For example, the figure below shows $3=\frac{1+5}{2}$, $8=\frac{5+11}{2}$ and $12=\frac{11+13}{2}$.
In the figure below, there are five overlapping circles and ten numbers are filled according to the conditions above. What is the sum of the numbers a and b?
In the figure below, there are five overlapping circles and ten numbers are filled according to the conditions above. What is the sum of the numbers a and b?