Blokkerende Botsauto's (2012)

Blokkerende Botsauto's (Blocking Dodgems) is a print and play game for two players. Each player is the driver of a car. The cars drive on a 4 by 4 grid of streets. Each player in turn passes one intersection. Each intersection is a double sided tile. One side has an intersection where no right turn is allowed. The other side shows an intersection where no left turn allowed. Driving straight ahead is always allowed. Each time a car has passed an intersection, its tile is flipped. The first player to pass all 16 intersections wins. The cars cannot be both on the same tile at the same time. A player who has nowhere to go (his car can only drive off the grid, or on a blocked tile) loses the game. During the setup phase of the game, each player determines the initial state of half of the grid. This game was published as a prize question in the Dutch magazine Pythagoras (issue 51/3, Jun 2012). It's a magazine about mathematics for high school students. Readers had to find a winning strategy (no answer was found).