The following pentagon is composed of 10 discs. Each disc must be filled with one number. The first 10 even positive numbers are allowed. The sum of the numbers to be placed in each side of the pentagon must be the same and the maximum possible. Find the sum of the numbers adjacent to the discs filled with the numbers 2 and 18.
The figure is shown below:
The choices given are:
I tried several ways to fill up this pentagon but did not find a clear solution. Does a strategy to solve this kind of puzzle exit? I'm stuck at the very beginning. I believe this requires mathematics. Please try to include some visual aid and the most detailed way to solve this problem.