A collection of $\displaystyle n$ couples attend a party at which a number

of people shake hands. Suppose that no pair shake hands more than once,

and no one shakes hands with her partner. At the end of the evening, the

host asks each of the $\displaystyle 2n-1$ other people how many hands they shook. She

receives $\displaystyle 2n - 1$ different answers. How many hands did the host shake?

How many did her partner shake?