Puzzle

[Saumyojit]

It seems you don't understand the problem. The 4 choices are independent. The situation described in #2 does NOT include conditions from #1, #3, #4.

what is the conculsion then

 

[Dr.Peterson]

Suppose acquaintance is not symmetric .
Guest 4 knows 1-3 guests . but it is given in the condition There is a person in the party who has an odd number of acquaintances . Guest 2 has already no of odd acquaintance.


YEs understood.
But if it is symmetric #2 is false BUT how can you say that ABC does not have three mutual acquaintances.

To reinforce what lev888 said, the four statements are not given conditions! In fact, you are told that one of them can never be true!

You are asked which of several possible conclusions is true: that there can never be someone who is acquainted with no one, and so on.

 

[lev888]

what is the conculsion then

My conclusion is that the aquaintance relationship is assumed to be symmetric and the correct answer is #2.

 

[Steven G]

How can there be a guest with zero acquaintances?
Why he is in the party? who has called him ? At least one acquaintance has to be there.

Maybe this person hosted the party. He/She invited people he did not know. Maybe he just moved onto the block and hosted a party to get to know everyone. This is not so crazy.

 

[Steven G]

(1)There is a person in the party who is acquainted with all the twenty-six others
The host of the party invites 26 of her friends.

(2)Each person in the party has a different number of acquaintances.
1 can be acquaintances with only 2---1 acquaintance
2 can acquaintances with only 1 and 3--2 acquaintances
3 can be acquaintances with 1, 2 and 4--3 acquaintances
4 can be acquaintances with 1, 2, 3 and 5--4 acquaintances
...
25 can be acquaintances with 1, 2, 3,...25 and 26---25 acquaintances
26 can be acquaintances with 1,2, 3, ... 25 and 27--26 acquaintances
27 can not be acquaintances with other than 1, 2, ..., or 26 acquaintances

(3)There is a person in the party who has an odd number of acquaintances
You have a party where you invite 25 of your closest friends and your new mate (who never met any of your friends). Then your mate will have exactly 1 acquaintance, namely you, and 1 is odd

(4)In the party, there is no set of three mutual acquaintances.
A new development has just opened. 14 families move in. 13 families consist of just a husband and wife. One family just has a female living there. No one outside their family knows anyone else. They all go to the get to know your new neighbors party. Does this party have three mutual acquaintances?

What do you think the answer is?