Adding the intersections of circles.

Question

Given the grid attached, how can you place the numbers $1-20$ at the intersections so that each circle adds to the same sum. I haven't been able to figure this out.

Answer 1

There are ten pairs of circles. Each pair meets in two points. If you make each matching pair sum to $21$ you will be done. Each circle goes through four pairs, so the sum will be $84$. Thinking about the symmetries of the problem is often a good place to start with these problems.