How many people are either a friend or a friend-of-a-friend of Ezhil?

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1	1	4	6
Bharatan				6
Chandran		1		6
Dhinesh			2	6
Ezhil			1	6
Fani	1			6
Gowtham	1	3	2	6

This table gives information about the number of strangers, acquaintances, and friends each person have.

Firstly, the total of every row will be 6.

Since, except the person himself, all other will be his acquaintances, friends or stranger.

Therefore, Amudha's friends = 6- 4 - 1 = 1

similairly, Gowtham's friends = 6 - 3 - 2 = 1

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1	1	4	6
Bharatan				6
Chandran	( G ,	1		6
Dhinesh			2	6
Ezhil			1	6
Fani	1			6
Gowtham	1 ( C )	3	2	6

Clue 3 says,

Chandran and Gowtham are friends.

We know Gotham has only one friend, which will be chandran

And , Chadran will also have gowtham as one of his friend.

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1	1	4	6
Bharatan	1	1	4	6
Chandran	( G ,	1		6
Dhinesh			2	6
Ezhil			1	6
Fani	1			6
Gowtham	1 ( C )	3	2	6

Clue 4 says,

Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.

Hence the number of acquaintances of Bharatan is equal to the number of friends of Amudha = 1

Similarly clue 5 says,

Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.

Hence the number of acquaintances of Amudha is equal to the number of friends of Bharatan.

Hence Bharatan has one friend, 1 Acquaintance, 4 strangers.

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1	1	4 (B, C	6
Bharatan	1	1	4 (A, C	6
Chandran	( G ,	1	(A, B	6
Dhinesh			2	6
Ezhil			1	6
Fani	1			6
Gowtham	1 ( C )	3	2	6

Clue 1 says,

Amudha, Bharatan, and Chandran are mutual strangers

=> For A , B and C are strangers

For B, A and C are strangers

and for C, B and A are strangers.

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1 ( E)	1	4 (B, C	6
Bharatan	1	1 ( E)	4 (A, C	6
Chandran	( G ,	1	(A, B	6
Dhinesh	(E,		2	6
Ezhil	(A, D, F	(B ,	1	6
Fani	1 (E )			6
Gowtham	1 ( C )	3	2	6

Clue 2 says,

Amudha, Dhinesh, and Fani are Ezil's friends.

=> A and E are mutual friends

D and E are mutual friends

and, F and E are mutual friends.

From this we can say that F and B will be acquittances. (According to clue 4)

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1 ( E)	1	4 (B, C, F	6
Bharatan	1	1 ( E)	4 (A, C, F	6
Chandran	( G ,	1	(A, B	6
Dhinesh	(E,		2	6
Ezhil	(A, D, F	(B ,	1	6
Fani	1 (E )		(A, B	6
Gowtham	1 ( C )	3	2	6

Now about Fani,

We know Fani has only 1 friend, which is Ezhil

Therefore, Fani will be a stranger to A & B.

As, If Fani is an acquaintance to Amudha

=> she will be friend to Bharatan (According to clue 6)

Which is not possible, as Fani has only Ezhil as friend.

Therefore, Fani has to be a stranger to both A and B.

And, A and B are strangers to Fani.

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1 ( E)	1	4 (B, C, F, G)	6
Bharatan	1	1 ( E)	4 (A, C, F, G)	6
Chandran	( G ,	1	(A, B	6
Dhinesh	(E,		2	6
Ezhil	(A, D, F	(B ,	1	6
Fani	1 (E )		(A, B	6
Gowtham	1 ( C )	3	2 ( A, B )	6

Similarly, about Gowtham :

We know Gowtham has only 1 friend, which is chandran.

Therefore, he will also be a stranger to A and B.

As, If Gowtham is an acquaintance to Amudha

=> he will be friend to Bharatan (According to clue 6)

Which is not possible, as Gowtham has only Chandran as friend.

Therefore, Gowtham has to be a stranger to both A and B.

And, A and B are strangers to Gowtham.

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1 ( E)	1 ( D)	4 (B, C, F, G)	6
Bharatan	1 ( D )	1 ( E)	4 (A, C, F, G)	6
Chandran	( G ,	1	(A, B	6
Dhinesh	(E, B )	( A, G )	2	6
Ezhil	(A, D, F	(B , G	1	6
Fani	1 (E )	( G,	(A, B	6
Gowtham	1 ( C )	3 ( D, E, F )	2 ( A, B )	6

Now we know, Amudha has only one acquaintance which will be now Dhinesh.

=> Dhinesh will be a friend of Bharatan (clue 6)

Similarly, for Gowtham, he has only 1 friend, which is C.

and only 2 strangers, which is A and B

=> D, E, F will be his acquaintances.

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1 ( E)	1 ( D)	4 (B, C, F, G)	6
Bharatan	1 ( D )	1 ( E)	4 (A, C, F, G)	6
Chandran	( G ,	1	(A, B, D	6
Dhinesh	2 (E, B )	2 ( A, G )	2 ( C, F)	6
Ezhil	(A, D, F	(B , G	1	6
Fani	1 (E )	( G,	(A, B, D	6
Gowtham	1 ( C )	3 ( D, E, F )	2 ( A, B )	6

We know, Dhinesh has 2 strangers

Also, we have found his 2 friends - E & B

and, his 2 acquaintances - A, G

=> He will have C & F as strangers.

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1 ( E)	1 ( D)	4 (B, C, F, G)	6
Bharatan	1 ( D )	1 ( E)	4 (A, C, F, G)	6
Chandran	( G ,	1 ( E )	(A, B, D, F)	6
Dhinesh	2 (E, B )	2 ( A, G )	2 ( C, F)	6
Ezhil	(A, D, F	(B , G , C)	1	6
Fani	1 (E )	1 ( G)	4 (A, B, D, F)	6
Gowtham	1 ( C )	3 ( D, E, F )	2 ( A, B )	6

Now, to C's arrangement, lets make cases :

CASE 1 - If C is a stranger to F -

=> F will have 4 strangers and one acquaintance which is G

=> C will also have 4 strangers and 1 acquaintance which will be E.

=> E and C will be acquaintance

=> E will have 3 acquaintance

But, we know, E already have 3 friends and 1 stranger

This will make the total of 7, which is not possible

Therefore, Case is rejected

=> C will be a acquaintance of F.

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1 ( E)	1 ( D)	4 (B, C, F, G)	6
Bharatan	1 ( D )	1 ( E)	4 (A, C, F, G)	6
Chandran	1 ( G )	1 ( F )	4 (A, B, D, E)	6
Dhinesh	2 (E, B )	2 ( A, G )	2 ( C, F)	6
Ezhil	3 (A, D, F)	2 (B , G )	1 (C )	6
Fani	1 (E )	2 ( G, C)	3 (A, B, D)	6
Gowtham	1 ( C )	3 ( D, E, F )	2 ( A, B )	6

Now, since C and F are acquaintance

=> F will have 1 friend, 2 acquaintance and 3 strangers = 6

Now, since, C has only 1 acquaintance which is F

and 1 friend, which is G

=> E and C will be strangers to each other.

=> E will have 3 friends, 2 acquaintances, and 1 stranger.

	No. of Friends	No. of Acquaintances	No. of Strangers	Total
Amudha	1 ( E)	1 ( D)	4 (B, C, F, G)	6
Bharatan	1 ( D )	1 ( E)	4 (A, C, F, G)	6
Chandran	1 ( G )	1 ( F )	4 (A, B, D, E)	6
Dhinesh	2 (E, B )	2 ( A, G )	2 ( C, F)	6
Ezhil	3 (A, D, F)	2 (B , G )	1 (C )	6
Fani	1 (E )	2 ( G, C)	3 (A, B, D)	6
Gowtham	1 ( C )	3 ( D, E, F )	2 ( A, B )	6

Friends are Amudha, Dhinesh and Fani. Also Dhani's friend Bhartan. So 4 is answer