Arrangement of Numbers to Get a Common Sum 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?

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.
