Science (incl math) is green. Blue is geography. Orange is sports. Pink is Entertainment. Art and Literature apparently can be either purple or brown. You’re still missing yellow for history.

There isn’t much math to do really. Take as axioms that the obvious way to balance 2 or 3 tubes is in fact balanced, and that if you add a balanced arrangement of tubes to an already balanced arrangement, the result is still balanced.

My problem seems to stem from the fact that my searches are often obscure and commercial interests probably wish I was searching for something else.