Both of the diagrams below include “nodes” connected by edges. Two nodes that are connected by an edge are said to be “adjacent”. For each diagram, place the integers 1, 3, 5, 7, 9, 11, and 13 in the nodes so that the positive differences between each pair of adjacent nodes are all different. As an example, a failed attempt is included for the first diagram.
Failed attempt for Diagram 1
The numbers above each of the edges in the failed attempt indicates the positive difference between the corresponding adjacent edges. As we can see, the positive differences are not all different (2 and 6 are repeated).