1) Create a planar factor graph with nodes numbered from 2 through 23.

2a) [easy] Show that no planar factor graph is possible with nodes numbered 2 through 32.

2b) [hard] Show that no planar factor graph is possible with nodes numbered 2 through 24.

3) If the nodes are numbered 1 though n, find the largest planar factor graph and prove that n+1 is impossible.

Tip: A finite graph is planar if and only if it does not contain as a subgraph either the complete graph K_{5} or the complete bipartite graph K_{3,3}.