Question 86
There is a row of 2018 squares, numbered consecutively from 0 to 2017. Initially a token is placed on square 0. Two players $A$ and $B$ play alternately, $A$ starting, as follows: on their turn, each player may either move the token forward 53 squares or move it back 2 squares, without ever going beyond square 0 or square 2017. The player who places the token on square 2017 wins. Which of them has a winning strategy, and how should that player play to make sure of winning?