MathDB
Numbers on blackboard

Source: Baltic Way 2016, Problem 13

November 5, 2016
combinatorics

Problem Statement

Let nn numbers all equal to 11 be written on a blackboard. A move consists of replacing two numbers on the board with two copies of their sum. It happens that after hh moves all nn numbers on the blackboard are equal to m.m. Prove that h≤12nlog⁡2m.h \leq \frac{1}{2}n \log_2 m.
Back to ProblemsView on AoPS