Given a $4\times 3$ chocolate cube, find the minimal number of divisions to break it into twelve $1\times 1$ cubes. Hint. The division process can be described by a graph. How many edges does this graph have?
I thought the reasoning is simple - any division process will take twelve steps because every division adds exactly one piece. But then, I don't understand why the analogous binary tree is relative, or how counting edges helps prove anything. What am I supposed to make of the hint?