MathDB

Let

S = {1, 2, 2^2, 2^3, ... , 2^{2021}}

. Compute the difference between the number of even digits and the number of odd digits across all numbers in

S

(written as integers in base

10

with no leading zeros). If E is the exact answer to this question and A is your answer, your score is given by

\max \, \left(0, \left\lfloor 25 - \frac{1}{2 \cdot 10^8}|E - A|^4\right\rfloor \right)

27