MathDB

Andrew starts with the

2018

-tuple of binary digits

(0,0,\dots,0)

. On each turn, he randomly chooses one index (between

1

and

2018

) and flips the digit at that index (makes it

1

if it was a

0

and vice versa). What is the smallest

k

such that, after

k

steps, the expected number of ones in the sequence is greater than

1008?

You must give your answer as a nonnegative integer. If your answer is

A

and the correct answer is

C

, then your score will be

\max\{\lfloor18.5-\tfrac{|A-C|^{1.8}}{40}\rfloor,0\}.

Problem Statement