MathDB
Romania Junior TST 2021 Day 2 P1

Source:

June 6, 2021
combinatoricsromaniaRomanian TSTgame

Problem Statement

On a board, Ana and Bob start writing 00s and 11s alternatively until each of them has written 20212021 digits. Ana starts this procedure and each of them always adds a digit to the right of the already existing ones.
Ana wins the game if, after they stop writing, the resulting number (in binary) can be written as the sum of two squares. Otherwise, Bob wins. Determine who has a winning strategy.