homework and exercises - Olympiad physics 1996 problem

I don't understand the official solution of the first problem of the 1996 International Physics Olympiad.

They give this circuit:

Each black box is a resistor of resistance $1\Omega$. They then claim that the following circuit is equivalent:

I no not see the equivalence. Why are these two equivalent and what principle(s) is(are) used to understand the equivalence?

Answer

Start with the initial diagram, but let's color code everything:

Now move some wires around, without actually changing the connectivity:

Finally, rotate the left and right blocks while again not changing the connectivity: