As an answer to Problem 3,
we give a Hamiltonian cycle (i.e., a cycle containing each vertex exactly once) of the giant component
of 266 vertices. Below is a starting configuration. By clicking "NEXT", you will get
a configuration that differs only by a legal move. After 266 clicks, you would have seen
all the 266 configurations in the giant component and have returned to the starting configuration.
Back to configuration #1