**Source:**Australian Mathematical Society Gazette - Puzzle Corner 28

**Problem:**

The Mad Hatter is holding a hat party, where every

guest must bring his or her own hat. At the party,

whenever two guests greet each other, they have to

swap their hats. In order to save time, each pair of

guests is only allowed to greet each other at most

once.

After a plethora of greetings, the Mad Hatter notices that it is no longer possible

to return all hats to their respective owners through more greetings. To sensibly

resolve this maddening conundrum, he decides to bring in even more hat wearing

guests, to allow for even more greetings and hat swappings. How many extra guests

are needed to return all hats (including the extra ones) to their rightful owners?

Other "Hat" Problems on the blog: