It is known that among the members of the government of Lemonia (and there are 20 members in total) there is at least one honest member, and that among any two members, at least one is a bribe-taker. How many bribe-takers are there in the government?

#
Note that in the government of Lemonia, there is exactly one honest official. Indeed, according to the condition, there is one honest official; but there cannot be two honest officials—otherwise, none of them would be a bribe-taker, which contradicts the condition. Therefore, there is exactly one honest official in the government, and thus, there are 19 bribe-takers.

## Answer

There are 19 bribe-takers in the government.