At a party, there are 2011 people with a glass of fruit juice each sitting around a circular table. Once a second, they clink glasses obeying the following two rules:
(a) They do not clink glasses crosswise.
(b) At each point of time, everyone can clink glasses with at most one other person.
How many seconds pass at least until everyone clinked glasses with everybody else?(Swiss Mathematical Olympiad 2011, Final round, problem 1) combinatorics proposedcombinatorics