Question 2.54

1. The -dimensional cube is obtained from two copies of an -dimensional cube by joining corresponding vertices. (The process is illustrated for the 3-cube and the 4-cube in the following figure.) Can you show that every n-cube has a Hamiltonian circuit? [Hint: Show that if you know how to find a Hamiltonian circuit on an -cube, then you can use two copies of this to build a Hamiltonian circuit on an -cube.]
   
2. Find formulas for the number of vertices and the number of edges of an -cube.