Question 13
A gem-collecting game consists of a robot and a map showing paths as below.
The robot starts at the starting position and keeps moving. At every three-way junction it stops to ask the controller which direction to turn. At a dead end it collects all the gems there.
Alex and Bob play together, taking turns to decide the robot’s turns. Alex wants to bring the robot to as many gems as possible; Bob wants the opposite. Both know each other’s goals and both reason very well. Alex makes the first decision. How many gems will the robot collect when it stops?
The robot starts at the starting position and keeps moving. At every three-way junction it stops to ask the controller which direction to turn. At a dead end it collects all the gems there.
Alex and Bob play together, taking turns to decide the robot’s turns. Alex wants to bring the robot to as many gems as possible; Bob wants the opposite. Both know each other’s goals and both reason very well. Alex makes the first decision. How many gems will the robot collect when it stops?