2019 BMT Individual Tiebreaker 3
Source:
January 9, 2022
combinatorics
Problem Statement
Ankit, Bill, Charlie, Druv, and Ed are playing a game in which they go around shouting numbers in that order. Ankit starts by shouting the number . Bill adds a number that is a factor of the number of letters in his name to Ankit’s number and shouts the result. Charlie does the same with Bill’s number, and so on (once Ed shouts a number, Ankit does the same procedure to Ed’s number, and the game goes on). What is the sum of all possible numbers that can be the rd shout?