This network has nine edges which meet at six nodes. The numbers 1, 2, 3, 4, 5, 6 are placed at the nodes, with a different number at each node. Is it possible to do this so that the sum of the 2 numbers at the ends of an edge is different for each edge?
image of 9 edges which meet at 6 nodes

Either show a way of doing this, or prove that it is impossible.

This problem is taken from the UKMT Junior Olympiad