MathDB

At first, on a board, the number

1

is written

100

times. Every minute, we pick a number

a

from the board, erase it, and write

a/3

thrice instead. We say that a positive integer

n

is persistent if after any amount of time, regardless of the numbers we pick, we can find at least

n

equal numbers on the board. Find the greatest persistent number.

Problem Statement