MathDB
BMT 2021 Guts Round p27

Source:

October 7, 2022
number theory

Problem Statement

Let S=1,2,22,23,...,22021S = {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 SS (written as integers in base 1010 with no leading zeros). If E is the exact answer to this question and A is your answer, your score is given by max⁡ (0,⌊25−12⋅108∣E−A∣4⌋)\max \, \left(0, \left\lfloor 25 - \frac{1}{2 \cdot 10^8}|E - A|^4\right\rfloor \right).
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