Arrangement of Numbers to Get a Common Sum

Question

I'm having trouble with a math problem. I need to arrange 6 numbers on a certain diagram:

At every intersection of two circles, I have to put one of these six numbers: 4, 5, 5, 6, 6, or 7. The sum of all of the numbers on each circle must be the same. Is it possible to arrange these numbers this way?

Answer 1

The sum of the numbers is $33$. Each occurs twice, total $66$. Three circles, four numbers adding up to $22$ on each. The $7$ must be matched with $6,5,4$. The $7$ is on the intersection of two circles; each of these circles must include a $4$; but there is only one $4$, so it must be on the other intersection of the same two circles. The rest is easy, and there are various solutions.

Answer 2

Edit: I misunderstood the question. Anyway, I'm keeping my answer here in case it provides additional ideas...

The sum of the numbers in each circle is 17.