blackboard numbers: a -> a:Ν mod N -> ... ->0 , sum of ... >100N
Source: Tournament of Towns, Junior A-Level Paper, Spring 2020 , p7
June 10, 2020
combinatoricsgameremainder
Problem Statement
Gleb picked positive integers and (). He wrote the number on a blackboard. Then each turn he did the following: he took the last number on the blackboard, divided the number by this last number with remainder and wrote the remainder onto the board. When he wrote the number onto the board, he stopped. Could he pick and such that the sum of the numbers on the blackboard would become greater than ?Ivan Mitrofanov