Question 57
Alina and Bogdan take turns, starting with Alina, writing a $0$ or a $1$ until each has written $2021$ digits. Each new digit is appended to the right of those already written.
Alina wins if the number represented by the resulting base-$2$ string, when expressed in decimal notation, can be written as the sum of two perfect squares; otherwise Bogdan wins. Determine which player has a winning strategy.
Alina wins if the number represented by the resulting base-$2$ string, when expressed in decimal notation, can be written as the sum of two perfect squares; otherwise Bogdan wins. Determine which player has a winning strategy.