Solution
Understanding the set :-
- Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people
- Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual.
This is a table set,
Here we need to find the number of strangers, acquaintances, and friends of every person.
In this set it is very important to understand that all the relations are mutual
=> for eg - if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.
| 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 |
As shown 3 Friends