Sum of numbers on board is bounded
Source: 43rd International Tournament of Towns, Senior O-Level P5, Fall 2021 & Kvant Magazine No. 11-12 2021 M2674
February 18, 2023
combinatoricsTournament of TownsProcessKvant
Problem Statement
Consider the segment . At each step we may split one of the available segments into two new segments and write the product of lengths of these two new segments onto a blackboard. Prove that the sum of the numbers on the blackboard never will exceed .Mikhail Lukin