MathDB

Vishal starts with

n

copies of the number

1

written on the board. Every minute, he takes two numbers

a, b

and replaces them with either

a+b

\min(a^2, b^2)

. After

n-1

there is

1

number on the board. Let the maximal possible value of this number be

f(n)

. Prove

2^{n/3}<f(n)\leq 3^{n/3}

Problem Statement