Question 95
Parliament has $76$ members and $114$ working groups (each has at least two members). There is no two working groups that have exactly the same members. If a member is elected as a speaker, he have to leave all his working groups and after that if there are two working groups that have exactly the same members, then the groups must be united into one working group. Prove that, it is possible that one can elect a speaker so that after the election there are at least $113$ working groups.
(proposed by B. Batbayasgalan)
(proposed by B. Batbayasgalan)