Question 9

Question 9 :
As they were moving through the jungle, they met an old drunkard who insisted everyone should to swap their hats. The troop contains 64 people. In order to save time, each pair within the troop swaps hat with each other only once (i.e. no swapping is repeated). After a round of madness, Tintin notices that it is no longer possible to return all hats to their respective owners through more swappings. To sensibly resolve this maddening confusion, he decides to bring in even more hat-wearing guests in his troop, to allow for even more hat swappings. How many extra guests are needed to return all hats (including the extra ones) to their rightful owners?
Note : Assume a person has exactly one mushroom.

I think its ans shud be 3.. Coz if we let those ppl sit in a circle n let the exchange begin, the initiator will get its hat back.. If we allow a guest n let ppl exchange caps with him, only one person will nt receive his hats back... To get the hats to their resp owner, we need 2 more guests.. So total 3..

Guess what i too got 3