(a) Create a digraph whose vertex set consists of three-digit binary sequences. From each vertex labelled xyz, there is one outgoing edge (labelled 0) leading to vertex yz0, and another outgoing edge (labelled 1) leading to vertex yz1.

A safe is locked by a combination of of four binary digits (that is, 0 or 1), but the
owner has forgotten the combination. The safe is designed in such a way that no
matter how many digits have been pressed, if the correct combination of three digits
is pressed at any point, then the safe automatically opens (there is no ”enter” key).
Our goal is to find the minimum number of digits that one needs to key in in order to
guarantee that the safe opens. In other words, we wish to find the smallest possible
length of a binary sequence containing every four-digit sequence in it.
(a) Create a digraph whose vertex set consists of three-digit binary sequences. From
each vertex labelled xyz, there is one outgoing edge (labelled 0) leading to vertex
yz0, and another outgoing edge (labelled 1) leading to vertex yz1.
(b) Explain why every edge represents a four digit sequence and why an Eulerian
tour of this graph represents the desired sequence of keystrokes.
(c) Find the minimum number of digits that one needs to key in to guarantee that
the safe opens.