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+5 votes
Consider that $15$ machines need to be connected in a LAN using $8$-port Ethernet switches. Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is ______
in Computer Networks by Veteran (425k points)
edited by | 2.9k views
3 is the answer i think
3 are required
Yeah, I also wrote 3 :0
how much marks for this question?
Can you explain how?
Which topic is this?


Can you please help me understand this question, please?

6 Answers

+12 votes
Best answer

.................. . 

Ans = 3

by Loyal (9.8k points)
selected by

@Tuhin Dutta

Plz tell me

what this line means

switches do not have any separate uplink ports

why 1 port interconnected? 

It means the links are duplex.
If ports are not interconnected how can all machines be connected?
Each and every node is connected to a machine and one single node is for connection to neighbor switch so that all machines are connected.
but in our home no switch is interconnected


Ethernet itself can give connection to the machine

isnot it?

Yes but here there are 15 machines. Let's give you an example - We have 3 labs Network lab, OS lab, and Programming lab. Each having 5 machines. Now we have to interconnect all of them. here comes the need for a switch. 

FYR please refer below

book Forouzan,  chp Introduction, sub-topic Network Types.

yes, I opened forouzan, but didnot find the line

"that switch need to be interconnected itself."


Can u plz mention the line of that book, where u find one extra switch need to interconnect other switches?

There's no such line but for interconnection, we need to connect the switches either by a router or directly using one of their port. Refer below images which are taken from Forouzan,5th edition.


The above two images hopefully will clear your doubt.

connection with circuit switching

Yes correct!


Ankit Bhai tell me something about this question?

I am  not able to get it.


@Tuhin Dutta

I have read that part from the Furouzon and it has nothing to do with this topic according to me.

Why do you think the question is related to that in any way?


+9 votes
There are 15 devices. And there are 8 ports in 1 Ethernet switch. So it's obvious that one switch is not sufficient. So one more switch is required. So in 1st switch only 7 ports are connected to 7 devices and 8th one is used for connecting to another switch. Now come to second switch. Only 7 ports are left as 1st port is used for connecting to 1st switch. Those 7 ports can be connected to 7 devices. But there are total 15 devices and so 1 would be left. So we need another switch. So now, in second switch we connect 6 devices to 6 ports and last port to third switch. And in the last switch 1st port is connected to 2nd switch and two ports to two left devices.So we require 3 switches in total.
by (455 points)
Finally, I understood from this answer.

+8 votes

So, Answer is $3$
by Junior (581 points)
edited by
is this question for 1 mark or 2 marks?
2 marks
+4 votes

Given :- A switch with $8$ ports and we require to connect $15$ machines together.

Using $1$ switch we can connect only $8$ machines together.


Using $2$ switches we can connect only $14$ machines together.


Using $3$ switches we can connect $20$ machines together.


$\therefore$ We require atleast $3$ switches to connect $15$ machines together.

by Boss (21.7k points)
edited ago by
$\mathbf {15}$ machines are given in the question and not $\mathbf{16}$
corrected, thankyou for correction :)


Actually I studied Switching but still not able to get the objective of this question.

Can you please tell me from which topic this belongs?


Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches

How will you break down this line?



I understood this answer.

Can you please now tell what to study to solve such question.

Is it a question of Switching theory, or LAN, or Ethernet?

This I am not able to get it.


Can you please tell me from which topic this belongs?

It is already mentioned in comments of best answer.

Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches

We have to make a LAN in which we will have 15 machines and they have to be connected using 8 port ethernet switches.


Below one right?

FYR please refer below

book Forouzan,  chp Introduction, sub-topic Network Types.


Honestly speaking , I didn't knew every concept related to this question but i just knew what a port means , from 8 port ethernet switches , the first figure made in answer came to my mind and rest was common sense.

Networking is the biggest theoritical subject of gate and you can't know everything from this subject in gate exam.So don't go too deep in every concept, they can ask anything.
Yeah, I understood it now that it is based on purely common sense. But I fear solving the question by looking at the answer isn't a great idea. Hence, I thought of going in and out.

Also, this is a previous year question which was already asked, so my objective was to learn from such questions as much as possible since I am now only solving pyq thoroughly.
Between thanks.

@jeet even i have problem with this topic..

correct me if i am wrong here:

Here it is given in the question that 15 computers need to be connected.. we can connect all 15 computers as shown in fig.a.

But we need to connect as shown in the figure.b attaining the same functionality as shown in figure a.

It is given that switch has 8 ports and it is given that there are no uplink ports. So all 8 ports can be used for connecting other devices.

we can connect  8 devices to a single switch .In that way ,we can connect 15 computers with 2 switches. but these 2 switches need to be connected so that all the devices are connected.

So we have to dedicate 1 port to connect with other switch..

Now you can refer satbir's answer.


Yeah I understood this basically, it is like this way:

M1 M2 M3 M4 M5 M6 M7 $\color{Red}{\mathbf{Ethernet-port1- out}}$


$\color{red}{\mathbf{Ethernet-port1- In}}$ M8 M9 M10 M11 M12 M13
$\color{red}{\mathbf{Ethernet-port2- out}}$


$\color{red}{\mathbf{Ethernet-port2- In}}$
M14 M15 M16 M17 M18 M19 M20


+3 votes
Out of 8 ports 1 port dedicated to the switch itself .hence 7 available ports for the clients.there are 15 clients s no of switches =3
by Junior (765 points)
0 votes

In LAN all the machines are interconnected. If we use a switch for 8 machines, and another for 7 machines; the first 8 machines won't be connected to the latter 7. So using two switches won't be enough.

In the first switch A,

  • First 7 ports — 7 machines.
  • Last port — Connect to other switch B.

In the second switch B

  • One port already connected to A
  • 6 ports — 6 machines
  • Last port — Connect to other switch C.

In the third switch C

  • One port already connected to B
  • 2 ports — 2 machines.

Done! We need 3 switches.



Machines to be connected = 15.

Ports available per switch = 7 (NOT 8)

So, 15/7 = 2.142 => 3 switches are required.

by Active (2.5k points)

Can you please explain this to me. I am not able to get the objective of this question.

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