Professionous Riddlous, society of 1+\sqrt{2n} members
Source: Iran National Olympiad - 2014 Second Round - D2P3
May 8, 2014
floor functionfunctioncombinatorics unsolvedcombinatorics
Problem Statement
Members of "Professionous Riddlous" society have been divided into some groups, and groups are changed in a special way each weekend: In each group, one of the members is specified as the best member, and the best members of all groups separate from their previous group and form a new group. If a group has only one member, that member joins the new group and the previous group will be removed. Suppose that the society has members at first, and all the members are in one group. Prove that a week will come, after which number of members of each group will be at most .