MathDB
TOT 1999 Spring AJ3 game with 1999 digits by only 0 and 1

Source:

May 11, 2020
combinatoricsgamegame strategy

Problem Statement

Two players play the following game. The first player starts by writing either 00 or 11 and then, on his every move, chooses either 00 or 11 and writes it to the right of the existing digits until there are 19991999 digits. Each time the first player puts down a digit (except the first one) , the second player chooses two digits among those already written and swaps them. Can the second player guarantee that after his last move the line of digits will be symmetrical about the middle digit?
(I Izmestiev)