2021-22 Winter Team #2
Source:
April 17, 2022
combinatorics
Problem Statement
A prefrosh is participating in Caltech’s “Rotation.” They must rank Caltech’s houses, which are Avery, Page, Lloyd, Venerable, Ricketts, Blacker, Dabney, and Fleming, each a distinct integer rating from to inclusive. The conditions are that the rating they give to Fleming is at most the average rating given to Ricketts, Blacker, and Dabney, which is in turn at most the average rating given to Avery, Page, Lloyd, and Venerable. Moreover are all integers. How many such rankings can the prefrosh provide?