How to solve the last dust machine puzzle in the chamber.?

The only real way is to be systematic. There are over 200 different possibilities so it would be hard to luck into this. There are 4 openings on the outer ring to accept dust from the collection device. Ther are 7 openings on the middle ring to accept dust from the outer ring, and there are 8 openings on the inner ring to accept dust from the middle ring. So select a position "1" on the outer ring to receive dust. The select a position "1" on the middle ring to receive dust from where it would come out of the outer ring. Then connect each of the 8 positions of the inner ring to receive dust from where dust would come out of the middle ring. If none of these work, move the middle ring to position 2 and so forth. When all of the positions on the middle ring have been tried, change the outer ring to position "2" and start over. Do this until every option has been exhauster. I succeeded when the outer ring was in it's last ("4th") position so it took me a while. I think it took me abou 20-30 minutes to hit on the right combination.