MathDB

Given several numbers, one of them,

a

, is chosen and replaced by the three numbers

\frac{a}{3}, \frac{a}{3}, \frac{a}{3}

. This process is repeated with the new set of numbers, and so on. Originally, there are

1000

ones, and we apply the process several times. A number

m

is called good if there are

m

or more numbers that are the same after each iteration, no matter how many or what operations are performed. Find the largest possible good number.

Problem Statement