How many handshakes occur when a group of 7 people shake hands exactly once with every other person in the group?

You are given two eggs, and access to a 100-storey building. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped from a floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, it cannot be used anymore.

If an egg breaks when dropped from floor N, then it would also have broken from any floor above that. If an egg survives a fall from floor N, then it will also survive any fall below floor N.

What is the minimum number of egg drops required to find the solution?

Every man in a village of 100 married couples has cheated on his wife. Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announces that at least one husband has been unfaithful. Everyone knows that the queen only speaks the truth. What happens?