How to solve a combinatorics problem?

Question

Mathematics

Recently I came across a very in my opinion problem in combinatorics. Since combinatorics was badly taught at school at one time, I can’t decide in any way. The second day I suffer. There are options. I will be extremely grateful if you help.

Answer 1

Represent circles with numbers as elements of the array [0..18]. You can sign them in the picture so as not to confuse anything. At the same time, for simplicity, the numbers 0, 1 and 2 can be assigned to circles with fixed numbers.
Compose 12 formulas - sums over circles and radii, of the form
x[0] + x[3] + x[4] + x[5] + x[6] + x[7]
x[1] + x[2] + x[8] + x[9] + x[10] + x[11]
etc.
Then recursively substitute into the array [3..18] combinations of 16 numbers from the remaining 17, calculate all the sums and check them for equality.