3. 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 longth of a binary so uence containing eueru four-digit sequen in it

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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3. 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 ryz, there is one outgoing edge (labelled 0) leading to vertex
yz0, and another outgoing edge (labelled 1) leading to vertex yz1l.
(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.
Transcribed Image Text:3. 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 ryz, there is one outgoing edge (labelled 0) leading to vertex yz0, and another outgoing edge (labelled 1) leading to vertex yz1l. (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.
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